# Question

The speeds of 2 trains A & B was in the ratio of 4:5. Train A started from Station P at 4.30 am and reached Station Q at 10.30 am. Train B left Station P, one hour later. How many mins before or after Train A did Train B reach Station Q?

pls kindly help. thanks.

# Answer

The speeds of 2 trains A and B was in the ratio of 4 : 5. Train A started from Station P at 4.30 am and reached Station Q at 10.30 am. Train B left Station P, one hour later. How many mins before or after Train A did Train B reach Station Q?

Speeds of train —
A : B
4 : 5

Time taken by train —
A : B
5u : 4u

4.30am ——- 6h ——- 10.30am
5u ——- 6h
1u ——- 6/5 = 1.2h
4u ——- 4 x 1.2 = 4.8h
4.30am ——- 1h ——- 4.8h ——- 10.18am
10.18am ——- 12min ——- 10.30am

Ans : 12 min before.
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This question is to “force” kids to understand and apply the relation between ratios of speed, distance and time, because there is no other information to use other methods. Unless one uses algebra to denote unknown distances or speed and proof by algebra, which I think is not what the setter intended.

A       :      B

Ratio of speed                            4       :       5

In same distance,

Ratio of time taken (note*)    5       :        4   (flip ratio–> Less speed, more time)

Actual time taken    “Given” 6 hrs   :  Solve for 4.8 hrs=4 h 48min   [=4units x 6hrs/5units]

Since Train B left 1 hour later than Train A, Train B reached Station Q at 10:18am (5:30am + 4h 48min)

(or Train B travelled for 1 hr 12 min less, but it has 1hr lag in start time. So left with 12 mins ahead of Train A)

Answer: Train B reached Station Q 12 mins before Train A#

[*Why ratio flipped:

Time taken T = Distance/Speed                      (Actual speed is 4s and 5s)

In same Distance D,

Ratio of time taken*                  D/4s       :        D/5s

(x 20)                   =        5 D/s       :       4 D/s

(Cancel D/s)       =           5            :         4    (Less speed, more time)]

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Hi SAHMOM, thank you so much for detail explanation.

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You are welcome. 🙂

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