Question

It takes You, riding a motorcycle, 2 hours less time to travel 60 miles than it takes Marley to travel 50 miles riding a horse. You travel 10 miles per hour faster than Marley on a horse. Find yours and Marley’s times and rates of travel. Hint: Set up a chart using d= rt

Answer 1

.......... D ..R ...T
You 60 x+10 60/(x+10)
Marley 50 x 50/x

50/x - 60/(x+10) = 2
times x(x+10)
50(x+10 - 60x = 2x(x+10)
50x + 500 - 60x = 2x^2 + 20x
2x^2 + 30x - 500 = 0
x^2 + 15x - 250 = 0
(x+25)(x-10) = 0
x = 10 or x = -25, the latter being silly

Marley went 10 mph on a horse, you went 20 mph on a bike
Marley spent 50/10 or 5 hrs
You spent 60/20 or 3 hrs, which is 2 hours less as needed

Answer 2

if the horse has speed h, and the motorbike has speed m, then since time = distance/speed,

60/m = 50/h - 2
m = h+10

60/(h+10) = 50/h - 2
60h = 50(h+10) - 2h(h+10)
2h^2 + 30h -500 = 0

Now you can find h, and then m=h+10