vaibhav101 wrote:John jogs 9 km at a speed of 6 km/hr. At what speed would she need to jog during the next 1.5 hrs to have an average speed of 9 km/hr for the entire jogging session?

A 9 km/hr
B 10 km/hr
C 12 km/hr
D 14 km/hr
E 15 km/hr

We use the formula: average speed = total distance/total time. We see that John has already jogged 9/6 = 1.5 hours. We can let his new speed be r km/hr for the next 1.5 hours and create the equation:

(9 + 1.5r)/(1.5 + 1.5) = 9

(9 + 1.5r)/3 = 9

9 + 1.5r = 27

1.5r = 18

r = 18/1.5 = 180/15 = 12

Answer: C

Hi vaibhav101,

We're told that John jogs 9 km at a speed of 6 km/hr. We're asked at what speed he would need to jog during the next 1.5 hrs to have an average speed of 9 km/hr for the entire jogging session. This is an example of a Weighted Average question - and since we're given all of the numbers to work with, it really just comes down to doing the necessary Arithmetic.

For the first part of the job, we can use the Distance Formula:
Distance = (Rate)(Time)
9 km = (6 km/hour)(X hours)
9/6 = X
X = 1.5 hours

Since the first 'leg' of the jog was 1.5 hours and the rest of the jog will be 1.5 hours, the TOTAL time for the entire job will be 3 hours. For an average speed of 9 km/hour for the ENTIRE jog, we can use the Average Speed Formula:
Total Distance = (Av. Speed)(Total Time)
Y miles = (9 km/hour)(3 hours)
Y = 27 miles

Since the first leg of the jog covered 9 km, we know that the rest of the job must cover 27 - 9 = 18 miles in 1.5 hours...

Distance = (Rate)(Time)
18 miles = (Z km/hour)(1.5 hours)
18/1.5 = Z
36/3 = Z
Z = 12 km/hour

Final Answer: C

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