Carcass wrote:
Jerry and Jim run a race of 2000 m. First, Jerry gives Jim a start of 200m and beats him by 30 seconds. Next, Jerry gives Jim a start of 3mins and is beaten by 1000m. Find the time in minutes in which Jerry and Jim can run the race seperately?
A. 8,10
B. 4,5
C. 5,9
D. 6,9
E. 7,10
Let's start with some
word equations Jerry gives Jim a start of 200m and beats him by 30 seconds. So,
Jerry runs 2000 meters, and
Jim runs 1800 meters.
Also, Jerry runs the race 30 seconds FASTER than Jim.
In other words, Jerry's travel time is 30 seconds (0.5 minutes) LESS THAN Jim's travel time
So, we can write: (
Jerry's travel time + 0.5 minutes) = (
Jim's travel time)
Let
R = Jerry's speed in meters per minute
Let
M = Jim's speed in meters per minute
time = distance/speed, so we can write:
2000/R + 0.5 =
1800/MTo eliminate the fractions, multiply both sides by MR to get: 2000M + 0.5MR = 1800R
Rearrange to get:
2000M = 1800R - 0.5MR Jerry gives Jim a start of 3mins and is beaten by 1000mThis time
Jerry runs 1000 meters, and
Jim runs 2000 meters.
Also, Jerry's travel time is 3 minutes LESS THAN Jim's travel time
So, we can write: (
Jerry's travel time + 3 minutes) = (
Jim's travel time)
time = distance/speed, so we can write:
1000/R + 3 =
2000/MTo eliminate the fractions, multiply both sides by MR to get: 1000M + 3MR = 2000R
Rearrange to get:
1000M = 2000R - 3MR We now have two equations:
2000M = 1800R - 0.5MR 1000M = 2000R - 3MR Take the bottom equation and multiply both sides by 2 to get:
2000M = 1800R - 0.5MR 2000M = 4000R - 6MR Since both equations are set equal to 2000M, we can now write: 1800R - 0.5MR = 4000R - 6MR
Rearrange to get: 5.5MR = 2200R
Divide both sides by R to get: 5.5M = 2200
Solve to get:
M = 400 meters per minutes (this is Jim's speed)
Time = distance/speed
So, time for Jim to run 2000 meters = 2000/400 = 5 minutes
Check the answer choices....only one answer choice has 5 minutes as Jim's running time
Answer: B