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.

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

twist boundary

explanation: