Alan and Brian start driving to their destinations at the same time. Alan travels #100# miles at an average of #60# miles per hour, while Brian travels #120# miles at an average of #75# miles per hour. Who arrives at their destination first?
1 Answer
The second car arrives
Explanation:
Let us convert the relevant fractions to have the same denominators.
The time in hours taken by each car is:
#100/60 = (5*color(red)(cancel(color(black)(20))))/(3*color(red)(cancel(color(black)(20)))) = 5/3 = (5*5)/(3*5) = 25/15#
#120/75 = (8*color(red)(cancel(color(black)(15))))/(5*color(red)(cancel(color(black)(15)))) = 8/5 = (8*3)/(5*3) = 24/15#
So the second car reaches its destination slightly earlier than the first car.
Alternatively, we can work in minutes:
The time taken for the first car in minutes will be:
#60*100/60 = 100#
The time taken for the second car in minutes will be:
#60*120/75 = (4 * color(red)(cancel(color(black)(15))) * 24 * color(red)(cancel(color(black)(5))))/(color(red)(cancel(color(black)(15))) * color(red)(cancel(color(black)(5)))) = 4 * 24 = 96#
