Bus 1 and Bus 2 run between cities A and B.
Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B,
each at a constant rate of speed. Their first meeting is 40 miles from city A. After reaching their
respective destinations and immediately turning around, their second meeting is 30 miles from city B.
What is the distance in miles between city A and city B?
Answer/Solution
90
Steps/Work
let d=distance between cities A and B
bus 1 distance to first meeting=40 miles
bus 1 distance from first to second meeting=(d-40)+30=d-10 miles
bus 2 distance to first meeting=d-40 miles
bus 2 distance from first to second meeting=40+(d-30)=d+10 miles
because both buses take the same time for the pre-meeting leg, and
the same time for the inter-meeting leg, and their speeds remain
constant, their ratios between pre-meeting distance and inter-meeting
distance should be the same
therefore, 40/(d-10)=(d-40)/(d+10)
d^2=90d
d=90 miles
A
bus 1 distance to first meeting=40 miles
bus 1 distance from first to second meeting=(d-40)+30=d-10 miles
bus 2 distance to first meeting=d-40 miles
bus 2 distance from first to second meeting=40+(d-30)=d+10 miles
because both buses take the same time for the pre-meeting leg, and
the same time for the inter-meeting leg, and their speeds remain
constant, their ratios between pre-meeting distance and inter-meeting
distance should be the same
therefore, 40/(d-10)=(d-40)/(d+10)
d^2=90d
d=90 miles
A