SOLUTION: Two runners are needed to get some medicine to a village 22 km away. The first runner starts the trip and runs for one hour. She then hands the medicine to the second runner, who t

Algebra ->  Linear-equations -> SOLUTION: Two runners are needed to get some medicine to a village 22 km away. The first runner starts the trip and runs for one hour. She then hands the medicine to the second runner, who t      Log On


   

Question 718798: Two runners are needed to get some medicine to a village 22 km away. The first runner starts the trip and runs for one hour. She then hands the medicine to the second runner, who takes it the rest of the way in 45 minutes. If the second runner runs 1.5 km/hr faster than the first, how fast was the first runner running? (Round off to the nearest whole number.)
a) 10 km/hr
b) 11 km/hr
c) 12 km/hr
d) 13 km/hr
How do I solve this problem?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
One way is to examine the first length and the second length and treat their sum.

First length: R%2A1 kilometers.
Second length: %28R%2B1.5%29%283%2F4%29 kilometers.

First length plus second length is 22 kilometers.
R%2B%28R%2B1.5%29%283%2F4%29=22 and solve for R from this. R is the slower runners speed.

R%2B%283%2F4%29R%2B1.5%283%2F4%29=22
%281%2B3%2F4%29R%2B9%2F8=22
%287%2F4%29R=22-9%2F8
R=%2822-9%2F8%29%284%2F7%29
R=%2820%267%2F8%29%284%2F7%29
R=%28167%2F8%29%284%2F7%29
R=167%2F14, R=11.9
Final Answer: R=12 kilometers per hour.