Expert: Bobby Soltani - 10/27/2005

Question
Stephen can ride to Grandma's house by bicycle in 3 hours. When he rides his snowmobile, the trip takes him 2 hours. If the snowmobile is 4 mph faster than the bike, how far is it to Grandma's house?

Answer
Hi Jeremy,

For this problem we need to know that distance traveled equals speed multiplied by time.

Stephen can ride to Grandma's house in 3 hours.  Let the distance to grandma's house be d, and the speed on a bicycle be s1.  Therefore, we can write

d = s1*3

If we let the speed of the snowmobile be represented by s2, we can write

d = s2*2

Since d = s2*2, we can substitute s2*2 for d in equation 1.

s2*2 = s1*3
divide both sides by 2

s2 = s1*(3/2)

We know that the snowmobile is 4 mph faster than the bike, so we can write

s2 = s1 + 4

We can substitute s1*(3/2) for s2 in this equation.

s1*(3/2) = s1 + 4
now we have 1 equation with 1 variable and we can solve it.

subtract s1 from both sides

s1*(3/2) - s1*(2/2) = 4
s1*(1/2) = 4
multiply both sides by 2

s1 = 8

now, we know that s2 = s1 + 4, so s2 = 4 + 8 = 12 mph

Let me know if you have any questions.

Bobby