Answer:
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
