Question 353719: After walking a distance of 6 miles at a certain rate, a man decided to increase his rate per hour by 1 mile and walked 5 miles farther. Had he walked the entire distance of 11 miles at his former rate, his time would have been 15 minutes longer. Find his former rate.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! After walking a distance of 6 miles at a certain rate, a man decided to increase his rate per hour by 1 mile and walked 5 miles farther.
-----
Had he walked the entire distance of 11 miles at his former rate, his time would have been 15 minutes longer. Find his former rate.
------------
1st segment DATA:
distance = 6 miles ; rate = x mph ; time = 6/x hrs.
------------------------
2nd segment DATA:
distance = 5 miles ; rate = x+1 mph ; time = 5/(x+1) hrs.
------------------------
Total distance DATA:
distance = 11 miles ; rate = x ; time = d/r = 11/x hrs
-------------------------------
Equation:
(time + time) - time = (1/4)hrs
[11/x] -[6/x + 5/(x+1)] = 1/4
---
Multiply thru by 4x(x+1) to get:
---
11*4(x+1) - [6*4*(x+1) + 5*4x] = x(x+1)
44x+44 - 24x-24 - 20x = x^2+x
20 = x^2+x
x^2+x-20 = 0
(x+5)(x-4) = 0
Positive solution:
x = 4 mph
------------------
Cheers,
Stan H.
|
|
|
