SOLUTION: Tom can run 5 miles in 1 hour less than the time required for David to run 4 miles. If tom is 4 mph faster than David, how many hours does each man run?

Question 895054: Tom can run 5 miles in 1 hour less than the time required for David to run 4 miles. If tom is 4 mph faster than David, how many hours does each man run?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Tom can run 5 miles in 1 hour less than the time required for David to run 4 miles. If tom is 4 mph faster than David, how many hours does each man run?
***
let x=David's speed
x+4=Tom's speed
Travel time=Distance/speed
..
(4/x)-5/(x+4))=1
lcd:x(x+4)
4(x+4)-5x=x(x+4)
4x+16-5x=x^2+4x
x^2+5x-16
solve for x by quadratic formula:

a=1, b=-5, c=-16
ans:
x≈-7.2 (reject)
or
x≈2.2
x+4≈6.2
..
4/2.2≈1.8 hrs
5/6.2≈0.8 hrs
how many hours does each man run?
Tom:0.8
David:1.8

RELATED QUESTIONS
if david can run 4 miles in 75 minutes what is david jogging rate per... (answered by amarjeeth123)

Jack can run 5 miles in the same time that Diane can run 4 miles. If Jack runs 2 mph... (answered by jorel1380,josgarithmetic,greenestamps)

Michael averaged running a certain distance 1 mph faster than David ran the same... (answered by josgarithmetic,MathTherapy)

I can bike 4 miles in the same amount of time as it takes my friend to run 3 miles. If I... (answered by lwsshak3)

tom can run 3 3/8 miles in 17 1/4 minutes, how long, on average,did it take him to run 1... (answered by bsitzmann)

David and Andrew are traveling to a Mathematics conference. David travels 110 miles in... (answered by Alan3354,greenestamps,josgarithmetic)

Stan can run 1 miles per hour, wheras Jack can run only 8 miles per hour. If they start... (answered by Alan3354)

Tom can ride 36 miles in the same time that Jerry can ride 24 miles. If Tom ride 9 mph... (answered by checkley71)

Tom can ride 36 miles in the same time that Jerry can ride 24 miles. If Tom ride 9 mph... (answered by Paul)