How do I solve this problem by using a rational expression?
Gomez commutes 50 miles on a motorbike to a technical college, but on the return trip he travels 15 miles per hour faster and makes the trip in 3/4 hour less time. Find Gomez’s speed to and from school.
Speed X time = distance
St = 50 …t = 50/S
S = speed, t = time…distance to and from is the same
St = (S + 15)(t – 3/4)
St = St – 3/4S + 15t – 45/4…….St cancels
0 = -3/4S + 15t – 45/4…….now substitute
0 = -3/4S + 15(50/S) – 45/4…….multiply by S
0 = -3/4S^2 + 750 – (45/4)S………multiply by -4
0 = 3S^2 – 3000 + 45S………divide by 3
S^2 +15S – 1000 = 0……..factor
(S + 40)(S – 25) = 0
S = -40, 25…….throw out negative
S = 25……….answer
t = 50/25 = 2……..answer
St = (S + 15)(t – 3/4)
25(2) = (25 + 15)(2 – 3/4)
50 = 40(5/4)
50 = 50
London motorcycle commuting – Honda CBF600.mp4
