SOLUTION: A tractor travels 10 miles in the same amount of time it takes a car to travel 15 miles. The rate of the tractor is 15 mph less than the rate of the car. Find the rate of the tra

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A tractor travels 10 miles in the same amount of time it takes a car to travel 15 miles. The rate of the tractor is 15 mph less than the rate of the car. Find the rate of the tra      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 403223: A tractor travels 10 miles in the same amount of time it takes a car to travel 15 miles. The rate of the tractor is 15 mph less than the rate of the car. Find the rate of the tractor.
Answer by rvquartz(19) About Me  (Show Source):
You can put this solution on YOUR website!
three key relationships for any vehicle in this case are:
(a) distance = (speed)(time)
(b) speed = distance /time
(c) time = distance /speed

for the car:
distance = d = 15 miles
speed = v
time = t

for the tractor:
distance = D = 10 miles
speed = v - 15
time = T

tractor time = car time, so

T = t

and using key relationship (c), we have:

10/(v-15) = 15/v

we can keep the equivalence if we multiply each side by the product of the denominators

10v = 15(v-15)
that is the same as
10v = 15v - 225

solving for v:

-5v = -225
5v = 225
v = 225/5
v = 45 miles per hour
V = v - 15 = 30 miles per hour

the rate of the tractor is 30 miles per hour