time apart

[wantitall]

2 buses leave St. Louis from the same station. one leaves at 5:00p.m. traveling north to Chicago at an average speed of 50mpg. the second leaves at 5:30 p.m. traveling south to New Orlenas, also at an average speed of 50 mph. at what time are they 325 miles apart?

[sddsddean]

8.30pm (making several assumptions)

[steve2010]

why dont you post this in quizzes and puzzles

[tim20054]

Whats the answer????

[dzug]

I'd have said 8.15.

At 530 they are 50 miles apart - only one bus has moved
At 630 they are 150 miles apart - they are going away from each other at a combined speed of 100mph
at 730 they are 250 miles apart, etc

[sddsddean]

At 5.30 the north bus has gone 25 miles, this leaves 300 miles. As they are travelling in opposite directions at 50mph, they are travelling apart at 100mph. therefore, 3 hours later at 8.30pm they are 325 miles apart. QED

[rja211077]

yes sddsddean is right. the mathematical way to solve it is:

d = 50t+50(t-0.5) (for t>0.5)

where d is the distance separating them in miles, t is the time elapsed since 5.00 in hours.

multiplying the brackets out:
d=50t+50t-25

simplifying:
d=100t-25

solving for d=325
325=100t-25
100t=350
t=3.5 hours elapsed since 5.00, therefore the time is 8.30

[dzug]

oops yes - a slight arithmetical/logical error there..... sorry