Question

Chuong and Hassan both drive 40 km from home to work each day. One day Chuong said to Hasssan, "If you drive home at your usual speed, I will average 40 kmph faster than you and arrive home in 20 minutes less time." Find Hassan's speed.

Answer 1

vt = d
d/v = t

Chuong claims he can go 40mph faster arrive
20 min is 1/3 of an hour earlier. (units have to match)

Hassans time (hours)
= 40/v
Choungs time (hours)
= 40/(v+40)
difference is 1/3

40/v - 40/(v+40) = 1/3
40/(v+40) = 40/v - 1/3
40/(v+40) = 120/3v - v/3v
40/(v+40) = (120-v)/3v
cross multiply
40(3v) = (v+40)(120-v)
120v = 120v -v^2 - 40v + 4800
cancel 120v on both sides
0 = -v^ - 40v + 4800
multiply all by -1
0 = v^2 + 40v - 4800
solving for v gives one positive solution 52.11 mph