Question

A man travels 10km in 50min if he runs for 8km and walks for 2km.if he runs 4km and walks 6km, his time is 1h15min.find his running and walking speed.

Answer 1

Change 50 min to 5/6 hr

Change 1 hr 15 min to 5/4 hr

:

Let r = his running speed in km/hr

Let w = his walking speed

:

Write a time equation for each scenario; time = dist/speed

:

8%2Fr + 2%2Fw = 5%2F6

and

4%2Fr + 6%2Fw = 5%2F4

:

Multiply the above by 2 and subtract the 1st equation

8%2Fr + 12%2Fw = 10%2F4

8%2Fr + 2%2Fw = 5%2F6

--------------------------------- subtraction eliminates r, find w

0 + 10%2Fw = 10%2F4 - 5%2F6

multiply by 12w, resulting in

12(10) = 3w(10) - 2w(5)

120 = 30w - 10w

120 = 20w

w = 120/20

w = 6 km/hr walking

:

Replace w with 6 in the 1st equation

8%2Fr + 2%2F6 = 5%2F6

8%2Fr = 5%2F6 - 2%2F6

8%2Fr = 3%2F6

cross multiply

3r = 8 * 6

3r = 489

r = 48/3

r = 16 km/hr running

:

;

Check solution in the 2nd equation

4%2F16 + 6%2F6 = 5%2F4