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

Answer:

Speed of train A is 44 miles/hr.

Step-by-step explanation:

Let the speed of train A = $u\ miles/hr$

Let the speed of train one = $v\ miles/hr$

Train A travels at $\frac{4}{5}^{th}$ the speed of train one.

i.e.

$u = \dfrac{4}{5}v \\\Rightarrow v =\dfrac{5}{4}u.... (1)$

Distance traveled = 693 miles

Time taken = 7 hours

They are travelling in opposite directions so the resultant speed will appear to be faster.

Relative speed = $u+v\ miles/hr$

The trains are 693 miles apart in 7 hours that means they have traveled a total distance of 693 miles in 7 hours with a speed of ($u+v$) miles/hr.

Using the formula:

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

$u+v = \dfrac{693}{7}\\\Rightarrow u+v=99 ...... (2)$

Putting the value of v using equation (1):

$\dfrac{5}4u+u=99\\\Rightarrow 5u+4u = 99 \times 4\\\Rightarrow 9 u = 99 \times 4\\\Rightarrow u = 11 \times 4 = \bold{44\ miles/hr}$

Speed of train A is 44 miles/hr.