Elimination Concept (3 Totals + 3 Variables)

First
Bags A, B, and C have candies inside them.
Bag A and Bag B have 69 candies.
Bag B and Bag C have 84 candies.
Bag C and Bag A have 79 candies.
a) How many candies are there in Bag C?
b) How many candies are there altogether?

Answer: (A: 32, B: 37, C: 47, Altogether 116)

Second
There are three candidates in a small town election: Obama, Mitt, and Donald.
Obama obviously won by a landslide. The votes were counted and it was revealed that Obama and Mitt won 1077 votes together, Mitt and Donald won 310 vote while Donald and Obama won 805 votes.

a) How many votes did Donald Trump win?
b) How many voters were there in that small town?

Answer: (Obama: 786, Mitt: 291, Donald: 19, Voters: 1096)

Third
There were three categories that contestants in a singing competition could compete in: Student, Adult and Group categories. Each contestant can only compete in only one category. There were 444 contestants in the Student and Adult categories.
On the other hand, there were 292 for the Student and Group categories.
For the Adult and Group categories, there were 308 entries.

a) How many students competed in the singing competition?
b) How many contestants were there in all?

Fourth
There are three classrooms in front of you.
The first and the second classrooms contain 59 students.
The second and the third classrooms contain 53 students.
The third and the first classrooms contain 50 students.
a) How many students are there in the second classroom?
b) How many students are there in the three classrooms altogether?

Answer: (A: 28, B: 31, C: 22, Altogether: 81)

Speed (Convergence + Difference in Distance)

Ali and Charles are both cycling to visit Bob.
They started from their houses at the same time and arrived at Bob's house at the same time.
The barber shop is located exactly halfway between Ali's and Charles' houses.
It is 140m from Bob's house.
Charles cycled at a speed 14m/min slower than Ali.
a) How much further did Ali cycle than Charles?
b) If Ali and Charles set off at 2pm, at what time did they arrive at Bob's house?

a) Difference in Distance = 140m × 2 = 280m

b) Shared Time = 280m ÷ 14m/min = 20min
End Time = 14 00 + 20min = 14 20 = 2.30pm

Concepts:
1) Difference in Distance (Convergence) = 2 x Distance of Meeting Point from Centre

2) Shared Time = Difference in Distance ÷ Difference in Speed

3) End Time = Start Time + Time Taken

Dan and Ellen started jogging at the same time along the same route.
Both did not change their speeds throughout.
After 35min, Dan was at the halfway point and Ellen was 300m behind.
Dan reached the end point 5 min before Ellen. What was the distance of the route?

300m × 2 = 600m
Ellen's Speed = 600m ÷ 5min = 120m/min
Halfway Distance = 120m/min × 35min + 300m = 4500m
Total Distance = 9000m

David and his brother John decided to cycle from his home to the library using the same route.
They started cycling at the same time. David cycled at a speed of 15km/h.
Both did not change their speed throughout the race.
When John covered 1/3 the distance, David was 4.5km ahead of him.
David reached the library at 4.45pm.
What time did John reach the library?

4.5km × 3 = 13.5km
13.5km ÷ 15km/h = 0.9h
= 0.9 × 60min = 54min
4.45pm + 54min = 5.39pm

A bakery and a library are 120 m apart. They are located between Hong's house and Jeya's house. The bakery is exactly half-way in between the two houses while the library is closer to Jeya's house. One day, Hong and Jeya started cycling from their houses at the same time and they arrived at the library together. Jeya cycled at 70 m/min while Hong cycled at a speed of 15 m/min faster than Jeya.

a) how much further did Hong cycle than Jeya?

b) how far is Jeya's house than the library?

Alex and Jack took part in a cycling race.
Jack cycled at a speed of 24km/h.
Both of them did not change their speed throughout the race.
When Alex reached the halfway point, Jack was 3km ahead of him.
Alex reached the end point at 12.10pm.
At what time did Jack reach the end point?

3km × 2 = 6km

6km ÷ 24km/h = 1/4 h = 1/4 × 60min = 15 min

12 10 - 15 = 11 55 = 11.55am

Speed Concepts (Divergence)

Given: Diverging Distance, Diverging Time, One Speed
Answer: Other Speed

First
Mr Lee and Mr Tan started driving from Point A in opposite directions. After driving for 4 hours, they were 660 km apart. If Mr Lee's driving speed was 100 km/h, find Mr Tan's average driving speed.


Given: Diverging Time, 2 Speeds
Answer: Diverging Distance


First
Timothy and Jane started jogging from the same place at the same time but in opposite directions along a straight road. Timothy's speed was 10km/h while Jane's speed was 8km/h. After jogging for 3 hours, how far apart were they?

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Total Speed = 10km/h + 8km/h
= 18km/h

Total Distance = 18km/h × 3h = 54km

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Given: Difference in Speed, Diverging Distance, Common Time
Answer: Fast or Slow Speed

First
Kerrine and Thompson started walking from the same starting point, but in opposite directions along a straight path.
Kerrine's average speed was 4 km/h more than Thomson's.
After walking for 3 hours, they were 40 km apart.
What was Kerrine's average walking speed.


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Difference in Distance = 4 km/h x 3 h = 12 km


Kerrine's Distance  = (40km + 12km) / 2 = 26 km


Kerrine's Speed = 26 km / 3 h = 8 2/3 km/h

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Second
Andy and Candy left their house at the same time and travelled in opposite directions.

Candy drove at a speed of 16km/h slower than Andy.
30 minutes later, Andy arrived at his destination, while Candy stopped for a rest.
They were 100km apart then.
Find Andy's speed.

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Difference in Distance = 16 km/h x 1/2 h = 8 km


Andy's Distance = (100 km + 8 km) / 2 = 54 km


Andy's Speed = 54 km / 1/2 h = 108 km/h

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