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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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       Log On


   

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(39616) About Me  (Show Source):
You can put this solution on YOUR website!
              SPEED          TIME               DISTANCE

regular           r           d%2Fr              d

faster            r+2        d%2F%28r%2B2%29           d

difference                   1%2F4

system%28d%2Fr-d%2F%28r%2B2%29=1%2F4%2Cd=200%29
substitute for d, simplify, and solve for r.

Answer by ikleyn(52776) About Me  (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


    200%2Fx - 200%2F%28x%2B2%29 = 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


    x%5B1%2C2%5D = %28-2+%2B-+sqrt%28%28-2%29%5E2+%2B+4%2A1600%29%29%2F2 = %28-2+%2B-+sqrt%286404%29%29%2F2 = -1+%2B-+sqrt%281601%29%29%2F2.


Of the two roots, only positive root x= -1+%2B+sqrt%281601%29 = 39.0125 is meaningful.


Answer.  His average speed is 39.0125 km/h  (approximately).


CHECK.   200%2F39.0125 - 200%2F%2839.0125+%2B+2%29 = 0.25.    ! Correct !

Solved.



Answer by math_helper(2461) About Me  (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:

+200%2Fr+=++200%2F%28r%2B2%29+-+%281%2F4%29+



Re-arranging and then simplifying:

++r%5E2+%2B+2r+-+1600+=+0+



Solving:

+r+=+-1+%2B-+sqrt%281601%29+ 



Taking positive result:    +highlight%28r+=+39.012%29+ 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.