Speed Concepts (Convergence)

Given: Total Distance, One Speed, Converging Time
Answer: Other Speed
First
Town A is 180 km away from Town B. John left Town A at 7.30 a.m., driving at a constant speed of 75km/h towards Town B. At the same time, Ali started driving from Town B to Town A. They passed each other at 8.50a.m.
a) What was Ali's average speed?
b) After passing Ali, John increased his speed by 5km/h. At what time did he reach Town B?

Method 1: Complement Distance
(John)
Method 2: Paired Speed
(Combined Journey)
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a) At what time did they meet each other? 
b) How far had each vehicle travelled when they met?
First
Second


Speed = 75km/h
Time Taken = 08 50 - 07 30 = 1hr 20min = 1 1/3hr
Distance = 100km

(Ali)
Distance = 180 - 100 = 80km
Time Taken = 1 1/3hr
Speed = 60km/h


Distance = 180km
Time = 1 1/3hr
Total Speed = 135km/h

Ali's Speed = Total Speed - John's Speed = 135 - 75 = 60km/h

Given: Total Distance, 2 Speeds
Answer: Converging Time

First

At 08 00, a car left Town A for Town B at a speed of 80 km/h. At the same time, a lorry left Town B for Town A at a speed of 70 km/h. The two towns were 375 km apart. 

Converging Speed = 80 km/h + 70 km/h = 150 km/h

Converging Time = 375 km / 150 km/h = 2 1/2 h

Meeting Time = 08 00 + 2 1/2 h = 10 30

Car Distance = 80 km/h x 2 1/2 h = 200 km

Lorry Distance = 70 km/h x 2 1/2 h = 175 km

Second

Town X and Town Y are 600 km apart. A car travels at an average speed of 90 km/h from Town X to Town Y. At the same time, a bus travels at an average speed of 60 km/h from Town Y to Town X. How far would each vehicle have travelled when they meet on their way?

Given: Total Distance, Time Taken, Difference in Speed

Happy Town and Merry City are 402 km apart. At 10 a.m., a lorry left Happy Town for Merry City. At the same time, a van set off from Merry City for Happy Town at an average speed that was 18 km/h faster than that of the lorry. Find the average speed of the van if the two vehicles met at 1 p.m.

Converging Time = 13 00 - 10 00 = 3 h

Converging Speed = 402 km / 3 h = 134 km/h

Van's Speed = (134 + 18) / 2 = 76 km/h

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Town A and Town B are 684km apart. At 10.45am, Jia Le drove from Town A to Town B. At the same time, Wei En drove from Town B to Town A. Both of the travelled at a constant speed throughout their journey. At 3.30pm, Wei En and Jia Le passed each other. If Jia Le was travelling at 18km/h slower than Wei En, what was Wei En's speed?


Converging Time = 15 30 - 10 45 = 4 h 45 min = 4 3/4 h
Converging Speed = 684 km / 4 3/4 h = 144 km/h
Wei En's Speed = (144 + 18) / 2 = 81 km/h

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Third
Wonder City and City of Dreams are 800 km apart. At 11.30 a.m , a car set off from Wonder City for City of Dreams, travelling at uniform speed. At the same time, a van left City of Dreams for Wonder City, also travelling at a uniform speed. At 4.30 p.m., the two vehicles passed each other. If the speed of the car is 22 km/h faster than the van, find the speed of the car.


Converging Time = 16 30 - 11 30 = 5 h
Converging Speed = 800 km / 5 h = 160 km/h
Car Speed = (160 + 22) / 2 = 94 km/h

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Convergence + Divergence 


First

At 9 a.m., a bus left Town C and travelled towards Town D at an average speed of 70 km/h. At the same time, a minivan left Town D and travelled towards Town C at an average speed of 55 km/h. At 11 a.m., the two vehicles were 35 km apart. If the two vehicles had passed each other by 11 a.m., find the distance between the two towns.

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Total Time = 11 00 - 09 00 = 2 h

Bus Distance = 70 km.h x 2 h = 140 km

Minivan Distance = 55 km/h x 2 h = 110 km

Town C to D Distance

= 140 km + 110 km - 35km

= 215 km

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Total Speed = 70 km/h + 55 km/h = 125 km/h

Diverging Time = 35 km / 125 km/h = 7/25 h

Total Time = 11 00 - 09 00 = 2 h

Converging Time = 2 h - 7/25 h = 1 18/25 h

Distance Between Town C and D

= 1 18/25 x 125 = 215 km

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Second
A car left Town A at 8 a.m., and travelled to Town B at an average speed of 60 km/h. At the same time, a lorry left Town B for Town A. At 11.30 a.m., the lorry and the car were 95 km apart after passing each other earlier. If the car arrived at Town B at 1 p.m., at what time would the lorry arrive at Town A?

Car's Total Time = 13 00 - 08 00 = 5 h
Town A to B Distance = 60 km/h x 5 h = 300 km
11 30 - 08 00 = 3h 30 min = 3 1/2 h
Car's Distance (at 11 30) = 60 km/h x 3 1/2 h = 210 km
Lorry's Distance (at 11 30) = 300 km - 210 km + 85 km = 175 km
Lorry's Speed = 175 km / 3 1/2 h = 50 km/h
Lorry's Total Time = 300 km / 50 km/h = 6 h
Lorry's Arrival Time = 08 00 + 6 h = 14 00


A bus travelled at a uniform speed from Town A to Town B. It passed a car which was travelling at a speed of 80 km/h in the opposite direction. 4 hours after they had passed each other, the bus reached Town B and the car was 30 km away from Town A. If the bus took 9 hours for the whole journey, find the distance between the 2 towns.


Car (Meeting to End) Distance = 80 km/h x 4 h + 30km = 350 km
Bus (Start to Meeting) Distance = 350 km
Bus (Start to Meeting) Time = 9 h - 4 h = 5 h
Bus Speed = 350 km / 5 h = 70 km/h
Bus (Start to End) Distance = 70 km/h x 9 h = 630 km

No Distance and No Speed (Assume Distance = 1 Journey)

First
Mr Tan took 6 hours to travel from Town A to Town B. Mr. Lim took 4 hours to travel from Town B to Town A. If both of them started travelling at 10 a.m., at what time did they pass each other?

Tan's Speed = 1/6 journey/hour

Lim's Speed = 1/4 journey/hour

Converging Speed = 1/6 + 1/4 = 5/12 journey/hour

Converging Time = 1 journey / 5/12 = 2 2/5 hour

Meeting time = 10 00 + 2 2/5 = 12 24

Second