A train leaves a city at 2 pm. A second train leaves a city at 4 pm and follows the first train the second train speed us 32 km/h faster than the first train speed. If the second train overtakes the first train at 8 pm, find the speed of both of the train

Given: A train leaves a city at $2:00\ pm$. A second train leaves a city at $4:00\ pm$ and follows the first train the second train speed up $32\ km/h$ faster than the first train speed. If the second train overtakes the first train at $8:00\ pm$.

To do: To find the speed of both trains.

Solution:

Let $A$ and $B$ are first and second trains. Let $x\ km/hr$ be the speed of first train $A$, then speed of train $B=( x+32)\ km/hr$.

At $8:00\ pm$ both second train overtakes the the first train.

Time taken by the first train $=6\ hr$

Time taken by second train $=4\ hr$

Distance covered by the first train$( A)=PQ=speed\times time=x\times x=6x$

Distance covered by the second train $( B)=PQ=speed\times time=( x+32)4$

$\because$ Distance covered by both train is same.

$\Rightarrow 6x=( x+32)4$

$\Rightarrow 6x=4x+128$

$\Rightarrow 6x-4x=128$

$\Rightarrow 2x=128$

$\Rightarrow x=\frac{128}{2}$

$\Rightarrow x=64$

Thus, The speed of first train$=x=64\ km/hr$

Speed of the second train$=x+32=64+32=96\ km/hr$

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Updated on: 10-Oct-2022

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