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A runner completed a 40 km race in 3 hours. She changed her speed after completing each quarter of the distance such that the proportion of the speeds in the first, second, third and the fourth quarter, is given by 2 : 3 : 4 : 5 respectively. In how much time then (approximately) did she complete the last quarter of the race ?
32 minutes
31 minutes
29 minutes
28 minutes
- Runner covers 40 km in 3 hours; thus, total time = 180 minutes.
- Each quarter is 10 km. The speed ratios are 2:3:4:5 for each quarter.
- Let speeds be 2x, 3x, 4x, 5x km/hr for each 10 km.
- Time for each: Distance/Speed.
1st: 10/(2x) = 5/x hours
2nd: 10/(3x) = 10/(3x) hours
3rd: 10/(4x) = 2.5/x hours
4th: 10/(5x) = 2/x hours
- Sum: (5/x) + (10/3x) + (2.5/x) + (2/x) = 3 hours
- In minutes: (5/x + 10/3x + 2.5/x + 2/x) × 60 = 180
- Combine: (5 + 10/3 + 2.5 + 2) = (5 + 3.33 + 2.5 + 2) = 12.83
- (12.83/x) = 3 ? x ˜ 4.28
- Time for last quarter = 10/(5x) = 2/x hours = (2/4.28)*60 ˜ 28 minutes.
Option 4: 28 minutes
By: santosh ProfileResourcesReport error
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