Mathematics: On a hike up hill, ted climbs at 3 miles an hour. going back down, he runs at 5 miles an hour. if it takes him forty minutes longer to climb up than run down, then what is the length of the hike?

On a hike up hill, ted climbs at 3 miles an hour.

kenleighbrooke67

12.03.2022

The length of hike is 5 miles.

Explanation

Suppose, the length of the hike is miles.

On a hike up hill, Ted climbs at 3 miles an hour and going back down, he runs at 5 miles an hour.

We know that, $Time= \frac{Distance}{Speed}$

So, the time taken by him to climb up $= \frac{x}{3}$ hours and the time taken by him to run down $= \frac{x}{5}$ hours.

Given that, it takes him 40 minutes longer to climb up than run down. Now, 40 minutes $=\frac{40}{60}hours=\frac{2}{3}$ hours.

So the equation will be......

$\frac{x}{3}-\frac{x}{5}=\frac{2}{3}\\ \\ 15(\frac{x}{3}-\frac{x}{5})=15(\frac{2}{3})\\ \\ 5x-3x=10\\ \\ 2x=10\\ \\ x=5$

So, the length of hike is 5 miles.

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beccastark1733

06.04.2021

1-may be it was so nice

Step-by-step explanation:

1916+1916=3832

hope it will help you

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