Question

Two trains leave New York at the same time heading in opposite directions. Train A travels at 4/5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A?

Answer 1

Given:

Two trains leave New York at the same time heading in opposite directions

Train A travels at 4/5 the speed of train one

After seven hours they are 693 miles apart

To find:

The speed of train A

Solution:

Let's assume,

"$\bold{S_A}$" miles/hr → Speed of the train A

"$\bold{S_1}$" miles/hr → Speed of the train 1

It is given that,

$S_A = \frac{4}{5}S_1$

$\implies S_1 = \frac{5}{4} S_A$

∴ Relative speed = $S_A + S_1$ = $S_A + \frac{5}{4}S_A$ = $\frac{9S_A}{4}$ ...... [since the trains are travelling in opposite directions]

After 7 hrs, the distance between train A and train 1 = 693 miles

Now, we have the formula as:

$Time = \frac{Distance}{Speed}$

Therefore, using the above formula, we can write eq. as

$7 = \frac{693}{S_A + S_1}$

$\implies 7 = \frac{693}{\frac{9S_A}{4} }$

$\implies \frac{9S_A}{4} = \frac{693}{7}$

$\implies \frac{9S_A}{4} = 99$

$\implies 9S_A = 396$

$\implies S_A = \frac{396}{9}$

$\implies \bold{S_A = 44\:miles/hr}$

Thus, the speed of train A is 44 miles/hr.

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