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06 Aug 2026, 04:04
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A delivery van traveled from Westport Depot to Lakeview Market in 7 hours. If the trip consisted of a 4-hour first leg at one constant speed and a 3-hour second leg at a different constant speed, what was the van’s average (arithmetic mean) speed for the entire trip?
(1) If the van had traveled for 8 hours at its first-leg speed and for 6 hours at its second-leg speed, it would have traveled 700 kilometers.
(2) If the van had traveled for 1 hour at each of those two speeds, it would have traveled 110 kilometers.
(1) If the van had traveled for 8 hours at its first-leg speed and for 6 hours at its second-leg speed, it would have traveled 700 kilometers.
(2) If the van had traveled for 1 hour at each of those two speeds, it would have traveled 110 kilometers.
06 Aug 2026, 04:04
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Official Solution:
A delivery van traveled from Westport Depot to Lakeview Market in 7 hours. If the trip consisted of a 4-hour first leg at one constant speed and a 3-hour second leg at a different constant speed, what was the van’s average (arithmetic mean) speed for the entire trip?
Let \(r\) be the van’s speed during the first leg, and let \(s\) be the van’s speed during the second leg.
The actual trip consisted of 4 hours at speed \(r\) and 3 hours at speed \(s\), so the total distance was:
\(4r + 3s\)
Since the trip lasted 7 hours, the average speed for the entire trip was:
\(\frac{4r + 3s}{7}\)
So we need the value of \(4r + 3s\).
(1) If the van had traveled for 8 hours at its first-leg speed and for 6 hours at its second-leg speed, it would have traveled 700 kilometers.
This gives:
\(8r + 6s = 700\)
Divide by 2:
\(4r + 3s = 350\)
Therefore, the average speed for the entire trip was:
\(\frac{350}{7} = 50\) kilometers per hour
Sufficient.
(2) If the van had traveled for 1 hour at each of those two speeds, it would have traveled 110 kilometers.
This gives:
\(r + s = 110\)
This does not determine the value of \(4r + 3s\).
Not sufficient.
Answer: A
A delivery van traveled from Westport Depot to Lakeview Market in 7 hours. If the trip consisted of a 4-hour first leg at one constant speed and a 3-hour second leg at a different constant speed, what was the van’s average (arithmetic mean) speed for the entire trip?
Let \(r\) be the van’s speed during the first leg, and let \(s\) be the van’s speed during the second leg.
The actual trip consisted of 4 hours at speed \(r\) and 3 hours at speed \(s\), so the total distance was:
\(4r + 3s\)
Since the trip lasted 7 hours, the average speed for the entire trip was:
\(\frac{4r + 3s}{7}\)
So we need the value of \(4r + 3s\).
(1) If the van had traveled for 8 hours at its first-leg speed and for 6 hours at its second-leg speed, it would have traveled 700 kilometers.
This gives:
\(8r + 6s = 700\)
Divide by 2:
\(4r + 3s = 350\)
Therefore, the average speed for the entire trip was:
\(\frac{350}{7} = 50\) kilometers per hour
Sufficient.
(2) If the van had traveled for 1 hour at each of those two speeds, it would have traveled 110 kilometers.
This gives:
\(r + s = 110\)
This does not determine the value of \(4r + 3s\).
Not sufficient.
Answer: A
