Isn't it a progression problem?

Algebra Level 2

A person starts from a place P to another place Q at a speed 30 k m p h 30 ~kmph . After every 12 minutes , he increases his speed by 5 k m p h 5 ~kmph . If the distance between P and Q is 51 km , then find the time taken by him to cover the whole distance (in minutes).

Source : JMO sample paper(2015)


The answer is 72.

Rishu Jaar by Rishu Jaar , 21, India

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1 solution

Francis Kong
Nov 11, 2017

One way to look at it is by intervals of 12 minutes due to the fact that changes happen every 12 minutes - If the required distance happen within one interval we can solve that part with simpler calculation.

One hour has 60 minutes and as such

30 k m h = 6 k m 12 m i n u t e s 30 \frac{km}{h} = 6 \frac{km}{12 minutes}

and for the speed increase

5 k m h = 1 k m 12 m i n u t e s 5 \frac{km}{h} = 1 \frac{km}{12 minutes}

Interval Speed (km/12 minutes) Distance travelled during interval(km) Total distance travelled(km)
1 6 6 6
2 7 7 13
3 8 8 21
4 9 9 30
5 10 10 40
6 11 11 51

Since at the end of the 6th interval we reach 51 km, t o t a l t i m e = 6 × 12 = 72 m i n u t e s total time = 6 \times 12 = \boxed{72} minutes

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution !(+1)

Rishu Jaar - 3 years, 7 months ago

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