LUANDATO wrote: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 50 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 B?

A) 90
B) 120
C) 125
D) 150
E) 180

We can PLUG IN THE ANSWERS, which represent the total distance between City A and City B.
When the correct answer is plugged in, the second meeting for the B� and B₂ will occur 30 miles from City B.

B: 120 miles
Since the buses meet for the first time 50 miles from City A, the first meeting is yielded by B� traveling 50 miles toward City B and by B₂ traveling 70 miles toward City A, as illustrated below by the figure for the first leg.
Implication:
Whenever B� travels 50 miles, B₂ travels 70 miles.

First leg:
B� travels 50 miles toward City B
Bâ‚‚ travels 70 miles toward City A
City A -----50----->B�...........70........... City B
City A ........50...........Bâ‚‚<---- 70------- City B

Second leg:
B� travels 50 more miles toward City B
Bâ‚‚ travels the remaining 50 miles to City A, turns around, and travels 20 miles toward City B, for a total of 70 miles
City A .............50................ ------50------>B� ......20......City B
City A <------50---------- .......................70...................... City B
City A -20->Bâ‚‚ .................................100............................City B

Third leg:
B� travels the remaining 20 miles to City B, turns around, and travels 30 miles toward City A, for a total of 50 miles
Bâ‚‚ travels 70 more miles toward City B
City A .............................100......................... --20--> City B
City A .....................90.............................B�<---30--- City B
City A ...20... ----------70------------>Bâ‚‚ .....30......City B

Success!
The second meeting for B� and B₂ occurs 30 miles from City B.

The correct answer is B.