SOLUTION: Kirk can bike 32 miles in the same amount of time that his twin brother Karl can bike 24 miles. If Kirk bikes 2 mph faster than Karl, how fast does each man bike?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Kirk can bike 32 miles in the same amount of time that his twin brother Karl can bike 24 miles. If Kirk bikes 2 mph faster than Karl, how fast does each man bike?       Log On


   

Question 1141376: Kirk can bike 32 miles in the same amount of time that his twin brother Karl can bike 24 miles. If Kirk bikes 2 mph faster than Karl, how fast does each man bike?
Found 3 solutions by josmiceli, MathTherapy, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for both to go 32 mi
Let +s+ = Karl's speed in mi/hr
+s+%2B+2+ = Kirk's speed in mi/hr
-------------------------------------------------
Karl's equation:
(1) +24+=+s%2At+
Kirk's equation:
(2) +32+=+%28+s%2B2+%29%2At+
-----------------------------
(2) +32+=+s%2At+%2B+2t+
and
(1) +s+=+24%2Ft+
Plug (1) into (2)
(2) +32+=+%28+24%2Ft+%29%2At+%2B+2t+
(2) +32+=+24+%2B+2t+
(2) +2t+=+8+
(2) +t+=+4+
and
(1) +s+=+24%2F4+
(1) +s+=+6+
and
+s+%2B+2+=+8+
------------------------
Karl's speed in 6 mi/hr
Kirk's speed is 8 mi/hr

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Kirk can bike 32 miles in the same amount of time that his twin brother Karl can bike 24 miles. If Kirk bikes 2 mph faster than Karl, how fast does each man bike?
Let Kirk's speed be S

Then Karl's speed is, S - 2

We then get the following TIME equation: matrix%281%2C3%2C+32%2FS%2C+%22=%22%2C+24%2F%28S+-+2%29%29

Solve this for S, Kirk's speed

SUBTRACT 2 from S to get Karl's speed

Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


(1) The ratio of the distances is 32:24 = 4:3.

(2) Since the times are the same, the ratio of the speeds is 4:3. So let the two speeds be 4x and 3x.

(3) The difference between the two speeds is 4x-3x = x. The problem tells us the difference in speeds is 2mph, so x = 2.

(4) So the two speeds are 4x = 8mph and 3x = 6mph.