Pablo can ride his bike 5 times as fast as jose can ride his bicycle. If it takes two hours longer to drive 15 miles, how fast can jose ride his bicycle

Question

word problem

 

 

Answer 1

distance = rate * time

 

If Pablo takes t hours to ride 15 miles

Then Jose takes (t+2) hours to ride 15 miles

 

Let Pablo's rate = P

Let Jose's rate = J

 

Pablo rides 5 times as fast as Jose so P = 5J

 

Pablo:  d = rt
15 = 5J(t)

 

Jose: d = rt

15 = J(t+2)

 

5Jt = Jt + 2J

4Jt = 2J

4t = 2

t = 0.5 hours

 

Since 15 = 5J(t)

5J(0.5) = 15

2.5J = 15

J = 6

 

Jose rides at 6 mph

Pablo rides at 5J = 30 mph