RTD problem unsolved - Anaïs completes a 20 km run in 1 hour 45 minute
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07 Feb 2023, 12:19
Hi,
I am studying for an exam that is the equivalent of the GMAT but in French (TAGE MAGE).
One of the practice questions is the following:
Anaïs completes a 20 km run in 1 hour 45 minutes. Anaïs starts the race quickly. After 2 km, her average speed drops. She takes 30 seconds more per kilometer compared to her average speed over the first two kilometers of the race. Finally, she accelerates over the last 5 km, which took her 11 minutes to complete. What is her approximate average speed from kilometer 2 to kilometer 15?
The solution is the following:
Let v be the average speed of Anaïs between the 2nd kilometer and the 15th kilometer.
T1=time spent on the first two km
T1 = distance/speed= 2/v + 1
T2=time spent between the 2nd km and the 15th km
T2=distance/speed = 13 / v
Anaïs takes 1 h 45 min - 11 min that is 94 minutes to cover the first 15 km, so : T1+T2=94minutes
2/v + 1 + 13/v = 94
=>15v=93
=>v=1593=3∗53∗31=531≈0,16
So Anais is going 0.16 kilometers per minute between the 2nd and 15th kilometers.
Does anyone understand why the distance spent on the first two km is 2 / v + 1 ?
Thank you in advance.