M46-36

Question

Three buses leave Riverton and travel along the same route toward Lakeview. Bus 1 leaves first and travels at a constant speed of 50 km/h. Bus 2 leaves Riverton 6 hours after Bus 1 and travels at a constant speed of 80 km/h. Bus 3 also leaves Riverton after Bus 1 and travels at a constant speed of 100 km/h. If Bus 2 and Bus 3 catch up to Bus 1 at the same time, how many hours after Bus 1 leaves does Bus 3 leave?

A. 2
B. 6
C. 8
D. 10
E. 16

Show Answer

Official Answer

C

A. 2
B. 6
C. 8
D. 10
E. 16

Bunuel · Answer

Official Solution:

Three buses leave Riverton and travel along the same route toward Lakeview. Bus 1 leaves first and travels at a constant speed of 50 km/h. Bus 2 leaves Riverton 6 hours after Bus 1 and travels at a constant speed of 80 km/h. Bus 3 also leaves Riverton after Bus 1 and travels at a constant speed of 100 km/h. If Bus 2 and Bus 3 catch up to Bus 1 at the same time, how many hours after Bus 1 leaves does Bus 3 leave?

A. 2
B. 6
C. 8
D. 10
E. 16

Show Answer

Official Answer

C

A. 2
B. 6
C. 8
D. 10
E. 16

Bus 2 leaves 6 hours after Bus 1, so by the time Bus 2 starts, Bus 1 has traveled:
 
 6 * 50 = 300  km
 
Thus, Bus 1 has a 300 km lead.
 
To catch Bus 1, Bus 2 needs:
 
 	ext{time} = \frac{	ext{distance}}{	ext{relative speed}} = \frac{300}{80 - 50} = 10  hours
 
So Bus 2 catches Bus 1:
 
 6 + 10 = 16  hours
 
after Bus 1 leaves.
 
In 16 hours, Bus 1 travels:
 
 16 * 50 = 800  km
 
Since Bus 3 catches Bus 1 at the same time, Bus 3 must also travel 800 km before catching Bus 1.
 
At 100 km/h, Bus 3 needs:
 
 \frac{800}{100} = 8  hours
 
Therefore, Bus 3 must have left:
 
 16 - 8 = 8  hours
 
after Bus 1 left.

Answer: C

M46-36

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