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Five friends decided to go for a race. The average time they completed the race was 64 minutes. The last finisher took 50 minutes more than the third finisher. The average time of the top two finishers was 40 minutes. The fourth finisher the race in 1 hour 20 minutes. Find the time (in minutes) in which the last finisher finished the race. 

Five friends decided to go for a race. The average time they completed the race was 64 minutes. The last finisher took 50 minutes more than the third finisher. The average time of the top two finishers was 40 minutes. The fourth finisher the race in 1 hour 20 minutes. Find the time (in minutes) in which the last finisher finished the race.  Correct Answer 105

Given:

The average time they completed the race was 64 minutes

The last finisher took 50 minutes more than the third finisher

The average time of the top two finishers was 40 minutes

The fourth finisher the race in 1 hour 20 minutes

Formula:

Average of n numbers a1, a2, ..., an = (a1 + a2 + ... + an)/n

Calculation:

Let the times they finished the race in be t1, t2, t3, t4 and t5 respectively

(t1 + t2 + t3 + t4 + t5)/5 = 64

⇒ t1 + t2 + t3 + t4 + t5 = 320

t5 = 50 + t3

⇒ t3 = t5 – 50

(t1 + t2)/2 = 40

⇒ t1 + t2 = 80

t4 = 60 + 20 = 80

Putting all the values in t1 + t2 + t3 + t4 + t5 = 320

80 + t5 – 50 + 80 + t5 = 320

2 × t5 = 320 – 110 = 210

∴ t5 = 105

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