Find Jose's average speed.

Question

Jose left the airport and drove toward the
lake. 0.9 hours later Mofor left driving
18.9 km/h faster in an effort to catch up to
him. After 2.6 hours Mofor finally caught
up. 

Answer 1

Remember that distance = rate × time. We'll write two equations, one for Jose and one for Mofor.

 

 

 

JOSE

 

We're not told how far Jose drove, so call that distance d. We're not told how fast Jose drove, so call that rate r. Jose drove for 0.9 hours and then another 2.6 hours, which is a total of 3.5 hours. So:

 

d = 3.5r

 

 

 

MOFOR

 

We're not told how far Mofor drove, but we know he caught up to Jose, so he drove the same distance d. We're not told how fast Mofor drove, but he drove 18.9 KPH faster than Jose, which is a rate of r + 18.9. Mofor drove for 2.6 hours. So:

 

d = 2.6(r + 18.9)

 

 

 

Now you have a system of two equations:

 

d = 3.5r

d = 2.6(r + 18.9)

 

Set the two equations equal to each other and solve for r:

 

3.5r = 2.6(r + 18.9)

3.5r = 2.6r + 49.14

0.9r = 49.14

r = 54.6

 

Jose drove at a rate of 54.6 KPH.