SOLUTION: Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour than Smith, and his trip took 1/2 hour longer than Smith's. How fast

Question 62053: Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour than Smith, and his trip took 1/2 hour longer than Smith's. How fast was each one traveling?
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
Let the speed of Smith be x mph
Then speed of Jones = (x+5) mph
Distance covered by Smith = 45 miles.
So time taken by Smith = Distance/time
= 45/x hrs
Distance covered by Jones = 70 miles.
Time taken by Jones = 70/(x+5) hrs.
By the given data,
70/(x+5) - 45/x = 1/2
Multiplying throughout by 2x(x+5) we get,
70*2x - 45*2(x+5) = x(x+5)
==> 140x - 90x - 450 = x^2 + 5x
==>50x - 450 - x^2 - 5x = 0
==> -x^2 + 45x - 450 = 0
==> x^2 - 45x + 450 = 0
==> x^2 - 15x - 30x + 450 = 0
==> x(x-15) - 30(x - 15) = 0
==> (x-15)(x-30) = 0
==> x-15 = 0 or x-30 = 0
==> x = 15 or x = 30
So either their speeds are 15 mph and 20 mph Or
their speeds are 30 mph and 35 mph respectively.
In either cases the difference in time taken = 1/2 hr.

Good Luck!!!

RELATED QUESTIONS
Smith bicycled 45 miles going east from Durango and Jones bicycled 70 miles. Jones... (answered by stanbon)

Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones... (answered by ankor@dixie-net.com)

Smith bicycled 45 miles goin east from Durango and Jones bicycled 70 miles. Jones... (answered by ankor@dixie-net.com)

Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones... (answered by stanbon)

Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70... (answered by ankor@dixie-net.com)

REPOST: Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones... (answered by 303795)

Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70... (answered by ankor@dixie-net.com)

solve. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles.... (answered by Paul,wuwei96815)

Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones... (answered by Paul)