Question

A cyclist 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 help me

Answer 1

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:

`d = 10t_1` (i)

Where
`t_1` is the time he traveled on the bicycle

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

`d = 3t_2` (ii)

Where
`t_2` is the time it took the cyclist to walk back home.

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

`t_1 + t_2 = 6.5` (iii)

We know from equation (i) that:

`t_1 = (d)/(10)`

We know from equation (ii) that:

`t_2 = (d)/(3)`

Then, substituting in (iii) we have:

`(d)/(10) + (d)/(3) = 6.5`.

We cleared d from the equation:

`(3d + 10d)/(30) = 6.5`

`13d = 195\\\\d = (195)/(13)\\\\d = 15 miles\\\\ t_1 = (15)/(10) = 1.5 h\\\\ t_2 = (15)/(3) = 5 h`

Answer:

The cyclist traveled on his bicycle a distance of 15 miles