Question

A man took a trip, traveling by train. He looked out the window during the first 1/3 of the trip. He then slept for 1/5 of the remaining distance. When he woke up read a book for 1/2 of the remaining of the distance. I f the train traveled 17.6 km more while he read than while he slept, how many km did the train travel

Answer 1

Answer: 528 km

Step-by-step explanation:

Let x be the total distance traveled by train.

Then, the total time he spent on looking outside the window and in sleeping = $\frac{x}{3}+\frac{x}{5}=\frac{8x}{15}$

Then the remaining distance =$x-\frac{8x}{15}=\frac{7x}{15}$

The time he spent on reading = $\frac{1}{2}\times(\frac{7x}{15})=\frac{7x}{30}$

Since, the train traveled 17.6 km more while he read than while he slept.

Then,

$\frac{7x}{30}-\frac{x}{5}=17.6\\\Rightarrow\ \frac{7x-6x}{30}=17.6\\\Rightarrow\ \frac{x}{30}=17.6\\\Rightarrow\ x=30\times17.6\\\Rightarrow\ x=528$

Hence, the train traveled 528 km.