# Question

Hi,

need help in the following question :

At 8am, Tom started travelling from Town A to Town B. At 8:40am, John started travelling from Town B to Town A. Tom’s speed and John’s speed were 45 km/h and 30km/h respectively. They did not change their speeds throughout the journey. When they met each other, their distance from Town A was twice their distance from Town B. Find the distance between Town A and Town B.

At 8:40am, Tom would have travelled 4/6 x 45= 30km.

The ratio of the Remaining distance covered by Tom : John =>45:30, as speed is proportional to distance.

Remaining distance= 45u + 30u, where Tom covered 45u and John covered 30u.

Total distance= 30 + remaining distance

Distance to town A is 30 + 45u and distance to town B is 30u and importantly distance to town A is twice of town B.

30 +45u = 2 x 30u

15u = 30

u=2

Total distance = 30 + 75u = 180km ##

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Not another answer. Just putting it in diagram, if it helps.

A picture  provides much clarity I think it explains the thought process very well.

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Thanks so much !

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At 8am, Tom started travelling from Town A to Town B. At 8:40am, John started travelling from Town B to Town A. Tom’s speed and John’s speed were 45 km/h and 30km/h respectively. They did not change their speeds throughout the journey. When they met each other, their distance from Town A was twice their distance from Town B. Find the distance between Town A and Town B.

(At 8 a.m., Mingwei started travelling from Town A to Town B.  At 8.40 a.m., Ali started travelling from Town B to Town A.  Mingwei’s speed and Ali’s speed were 45 km/h and 30 km/h respectively.  They did not change their speeds throughout the journey.  When they met each other, their distance from Town A was twice their distance from Town B.  Find the distance between Town A and Town B.)

Town A                             Town B
l ——- 1 ——- 1——- 1
Tom (Mingwei)               John (Ali)
8am                                8.40am
45km/h                           30km/h

8am to 8.40am ——- 40min
45 x (40/60) = 30km
30 + 45t = 30t x 2
t = 30/(60 – 45) = 2
30 + 45t + 30t = 180

Ans : 180km.

i don’t understand this equation.

30 + 45t = 30t x 2
t = 2
30 + 45t + 30t = 180

what is t? how did u get t=2?

what is the distance to town b is 30t x 2?

i don’t understand this equation. (Use average speed x time taken= distance travelled)

30 + 45t = 30t x 2 ( Tom who started travelling from Town A to Town B at 8am had a 30km head start as compared to John who started travelling from Town B to Town A only at 8.40am plus Tom’s speed of 45 km/h x time taken = John’s speed of 30km/h x 2. When they met each other, their distance from Town A was twice their distance from Town B.)
t = 2
30 + 45t + 30t = 180

what is t? (t is time taken)

how did u get t=2?

(30 + 45t = 30t x 2
t = 30/(60 – 45) = 2)

what is the distance to town b is 30t x 2? (When they met each other, their distance from Town A was twice their distance from Town B. Have I answered your questions adequately?)