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

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06-02-2019
Mathematics

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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

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JeanaShupp JeanaShupp · Answer 1 · 2019-02-19T07:26:02+01:00

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 = [tex]\frac{x}{3}+\frac{x}{5}=\frac{8x}{15}[/tex]

Then the remaining distance =[tex]x-\frac{8x}{15}=\frac{7x}{15}[/tex]

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

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

Then,

[tex]\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[/tex]

Hence, the train traveled 528 km.