Acyclist rides into the country at an average speed of 10 miles per hour. when his bicycle gets a flat tire, he walks it back at an average speed of 3 miles per hour. if he returns home 6 and a half hours after he starts, how far into the country does he go? pls me

To solve this problem you must analyze the data provided very well.

The distance the cyclist travels across the country is the same as when he travels back home. Let's call d at that distance.

The distance traveled when the cyclist travels on the bicycle is:

(i)

Where is the time he traveled on the bicycle

Now, the distance traveled by the cyclist back home is:

(ii)

Where is the time it took the cyclist to walk back home.

The total time that the tour lasted was 6.5 hours. So:

(iii)

We know from equation (i) that:

We know from equation (ii) that:

Then, substituting in (iii) we have:

.

We cleared d from the equation:

The cyclist traveled on his bicycle a distance of 15 miles

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