SOLUTION: Vehicle A which is ahead of vehicle B by 2/3 mile is traveling at 53 mph. Vehicle B which is behind vehicle A is traveling 75 mph. How long and how far will it take vehicle B to ca

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Question 757384: Vehicle A which is ahead of vehicle B by 2/3 mile is traveling at 53 mph. Vehicle B which is behind vehicle A is traveling 75 mph. How long and how far will it take vehicle B to catch vehicle A?
Same question but with A going 30 mph.
Answer by lwsshak3(11628) (Show Source):
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Vehicle A which is ahead of vehicle B by 2/3 mile is traveling at 53 mph. Vehicle B which is behind vehicle A is traveling 75 mph. How long and how far will it take vehicle B to catch vehicle A?
Same question but with A going 30 mph.
***
let x=distance A traveled
x+2/3=distance B traveled to catch A
travel time=distance/speed (same for A and B)
..

75x=53x+(106/3
22x=106/3
x=106/66
x≈1.6
x+2/3≈2.27
travel time=1.6/53=.03 hr or≈1.81 min
B will catch up to A in 1.81 min after traveling 2.27 mi
..
For A going 30 mph

75x=30x+20
45x=20
x=20/45
x≈0.44
x+2/3≈1.11
travel time=0.44/30=.015hr or≈0.89 min
B will catch up to A in 0.89 min after traveling 1.11mi