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Running on a 10-mile loop in the same direction, Sue ran at
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14 Jun 2018, 14:39
14 Jun 2018, 14:39
Expert Reply
4
Bookmarks
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Question Stats:
69% (01:20) correct
30% (01:21) wrong based on 92 sessions
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Running on a 10-mile loop in the same direction, Sue ran at a constant rate of 8 miles per hour and Rob ran at a constant rate of 6 miles per hour. If they began running at the same point on the loop, how many hours later did Sue complete exactly 1 more lap than Rob?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Re: Running on a 10-mile loop in the same direction, Sue ran at
[#permalink]
07 Jul 2018, 04:28
07 Jul 2018, 04:28
1
Expert Reply
Explanation
If Sue completed exactly one more lap than Rob, she ran 10 more miles than Rob. If Rob ran d miles, then Sue ran d + 10 miles. Rob and Sue began running at the same time, so they ran for the same amount of time. Let t represent the time they spent running. Fill out a chart for Rob and Sue, using the formula Distance = Rate × Time (D = RT):
There are two equations:
\(d = 6t d + 10 = 8t\)
Substitute 6t for d in the second equation and then solve for t:
\(6t + 10 = 8t\)
\(10 = 2t\)
\(5 = t\)
Hence option C is correct!
If Sue completed exactly one more lap than Rob, she ran 10 more miles than Rob. If Rob ran d miles, then Sue ran d + 10 miles. Rob and Sue began running at the same time, so they ran for the same amount of time. Let t represent the time they spent running. Fill out a chart for Rob and Sue, using the formula Distance = Rate × Time (D = RT):
| D(miles) | = | R(miles per hour) | \(\times\) | T (hours) | |
| Rob | d | = | 6 | \(\times\) | t |
| Sue | d+10 | = | 8 | \(\times\) | t |
There are two equations:
\(d = 6t d + 10 = 8t\)
Substitute 6t for d in the second equation and then solve for t:
\(6t + 10 = 8t\)
\(10 = 2t\)
\(5 = t\)
Hence option C is correct!
Re: Running on a 10-mile loop in the same direction, Sue ran at
[#permalink]
04 Nov 2018, 08:11
04 Nov 2018, 08:11
2
Difference in distance/Difference in speeds = 10/(8-6) = 5
