The tourist rode a moped from point M to point N at a speed of 50 km. 24 minutes after leaving M

| May 14, 2021 | education

The tourist rode a moped from point M to point N at a speed of 50 km. 24 minutes after leaving M, his speed dropped by 10 km / h as the road went uphill. As a result, the tourist arrived at N. 18 minutes later than expected. How many kilometers did the tourist travel?

We take the time during which the tourist planned to travel the path for x.

Then the whole path is 50x km;

The speed on the second part of the path is 40 km / h;

Actual travel time (х + 18/60) h;

Let’s compose and solve the equation:

50 * (24/60) + 40 * ((x + 18/60) – (24/60)) = 50x;

(50 * 24) / 60 + 40 * (60x + 18 – 24) / 60 = 50x;

Let’s get rid of the fraction by multiplying each term in the equation by 60 and reducing by 10;

5 * 24 + 4 * (60x – 6) = 50x * 6;

120 + 240x – 24 = 300x;

x = 96/60;

The distance is 50 * (96/60) = 90 km.



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