Algebra World Problem

Question

Will and Jim shared a driving trip from Beaufort to a business convention 352 miles away. Will’s
average speed was 52 miles per hour. Jim averaged 44 miles per hour and drove 2 hours longer
than Will. How far did Jim drive?

Answer 1

First we will remember that: Distance = Velocity (average) * Time

 

Lets assign the following: X = time Will drive in hours; Y = time Jim drives in hours

 

First equation: 52mph*X + 44mph*Y = 352 miles

 

Second equation: Y = X + 2

 

Substitute Second equation into First

 

52mph*X + 44mph*(X+2) = 352 miles

52mph*X + 44mph*X + 88 miles = 352 miles

96mph*X = 352 - 88 miles

96mph*X = 264 miles

X = 264 miles/96mph

X = 2.75 hours

 

Y = 2.75 hours + 2 hours = 4.75 hours

 

Jim drove 4.75 hours at an average velocity of 44mph

Distance = 44mph*4.75 hours = 209 miles

 

Will drove 2.75 hours at an average velocity of 52mph

Distance = 52mph*2.75 hours = 143 miles

 

Cross check:

Total Distance: 209 + 143 = 352 miles...