John runs for 10 min at a uniform speed of 9 km/h. At what speed he should run for the next 20 min, so that the average speed comes 12 km/h?
Answers
Given that, the John runs for 10 min at a uniform speed of 9 km/hr.
We have find the speed of the John with which he should run for the next 20 min, so that the average speed comes 12 km/hr.
Now,
Average speed is defined as the ratio of total distance covered with respect to total time taken.
Let's assume that the speed of the John in next 20 min is x km/hr.
Total distance covered by John = (9 + x)km
Total time taken = (10 + 20) min = 30 min = 1/2 hr.
Average speed = 12 km/hr (given)
Also,
Distance = Speed × Time
d1 = 9 × 1/6 = 1.5 km
d2 = x × 1/3 = x/3 km
Average speed = (Total distance covered)/(Total time taken)
Substitute the known values,
→ 12 = (1.5 + x/3)/(1/2)
→ 6 = 1.5 + x/3
→ 6 - 1.5 = x/3
→ 4.5 = x/3
→ 13.5 = x
Therefore, the speed of the John in next 20 min is 13.5 km/hr.
Given:
- John runs uniform speed of 9km/h for 10min
To find:
- Speed of John for next 20 min so that average speed becomes 12km/h
Solution:
Covert min → hrs
10min → 0.16 hrs
20min → 0.33
Let distance covered by John by next 20min be x
So,
Total distance = 9km + x km
Total time = 10min + 20min = 30min = 1/2hr
Avg speed for 10min = 12km/h
Now,
Distance = speed × time
Distance 1 = 9 × 0.166 = 1.5
Distance 2 = x × 0.33 = 0.33x = x/3
Total distance = d1 + d2
→ Total distance = 1.5 + x/3
→ d1 + d2 = 1.5 + x/3
Now,
Average speed = d1 + d2/t1 + t2 = total distance/total time
♦ Avg speed = (1.5 + x/3)/1/2
♦ 12 = (1.5 + x/3) × 2
♦ 12 = 3 + 2x/3
♦ 36 = 9 + 2x
♦ 36 - 9 = 2x
♦ x = 25/2
♦ x = 12.5
Hence, speed of John = 12.5km/h