SOLUTION: On a journey of 200 km, a motorist found that if he were to increase his average speed by 2 km/h, the journey would take 15 minutes less. Calculate his average speed

Question 1137736: On a journey of 200 km, a motorist found that if he were to increase his average speed by 2 km/h, the journey would take 15 minutes less. Calculate his average speed
Found 3 solutions by josgarithmetic, ikleyn, math_helper:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE regular r d faster r+2 d difference

substitute for d, simplify, and solve for r.
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

Let x be his average speed (in km/h). Then from the condition you have this "time" equation - = 0.25 of an hour (0.25 = 0.25 hour = 15 minutes) To solve it, first multiply both sides by 4x*(x+2). You will get 800*(x+2) - 800x = x*(x+2) 1600 = x*(x+2) x^2 + 2x - 1600 = 0 = = = . Of the two roots, only positive root x= = 39.0125 is meaningful. Answer. His average speed is 39.0125 km/h (approximately). CHECK. - = 0.25. ! Correct !

Solved.

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

d=rt
Using units of hours for time, km for distance:
r=d/t = 200/t (1)
We are given:
r+2 = d/(t-1/4) (2)
Solving each for t and then setting them equal to eliminate t:

Re-arranging and then simplifying:

Solving:

Taking positive result: km/hr
-----------
Check: Add 2km/hr to the above: 41.012 km/hr
At 39.012km/hr the trip takes 200km/(39.012km/hr) = 5.1266hr
At 41.012km/hr the trip would take 200km/(41.012km/hr) = 4.8766hr
The difference is 0.25hr which is 15 minutes.

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