SOLUTION: Albert and Bob ran a race of 440 yards. In the first trial albert gave bob a start of 65 yards and won by 20 seconds. In the second trial albert gave bob a start 34 seconds and bo

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Question 976188: Albert and Bob ran a race of 440 yards. In the first trial albert gave bob a start of 65 yards and won by 20 seconds. In the second trial albert gave bob a start 34 seconds and bob won by 8 yards. Find the speeds of albert and bob in yards per second
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Albert and Bob ran a race of 440 yards.
In the first trial Albert gave bob a start of 65 yards and won by 20 seconds.
In the second trial Albert gave bob a start 34 seconds and bob won by 8 yards.
Find the speeds of Albert and bob in yards per second
:
let a = Al's running speed (yds/sec)
let b = Bob's speed
:
Write a time equation for each scenario; time = dist/speed
:
A runs 440 yds while b runs 440 - 65 = 375 yds, beats him by 20 sec
b's time - a's time = 20 sec
375%2Fb - 440%2Fa = 20
:
b's travels 440 - 8 = 432 yds, while a travels 440 yds in 34 sec less time
432%2Fb - 440%2Fa = 34
subtract the 1st equation from the 2nd equation
432%2Fb - 440%2Fa = 34
375%2Fb - 440%2Fa = 20
--------------------------------subtraction eliminates a, find b
57%2Fb = 14
b = 57%2F14
b = 4.07 yds/sec is Bob's speed
:
Find a using the 1st equation
375%2F4.07 - 440%2Fa = 20
92.1376 - 440%2Fa = 20
-440%2Fa = 20 - 92.1376
-440%2Fa = -72.1376
440%2Fa = 72.1376
a = 440%2F72.1376
a = 6.1 yds/sec is Al's speed
:
:
Check this in the 2nd equation
432%2F4.07 - 440%2F6.1 = 34
106.14 - 72.13 = 34.0 sec