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Maths Problem

Derek drove 30 km in a time of x minutes. He then drove a further 50km in (x+10) minutes. When he calculated his speed, he found that his average speed for the first section of the journey was 6km per hour less than his average speed for the whole journey.

(a) Express 6km per hour in km per minute
(b) Make an equation and solve it to find two possible values of x. State which value is more likely to be correct for this problem.

Thanks in advance

Reply 1

SsEe

6 km/h = 6/60 = 0.1 km/min

average speed is 80 / (2x + 10) = 40/(x+5) (total distance / total time)
Speed in part one = 40/(x+5) - 0.1
s = d/t
40/(x+5) - 0.1 = 30/x
multiply up by x(x+5)
40x - 0.1x(x+5) = 30(x+5)
Expand and simplify:
0.1x² - 9.5x + 150 = 0
x² - 95x + 1500 = 0
(x - 75)(x - 20) = 0
x = 75 mins or x = 20 mins

If x = 20 then his average speed is 96 km/hour, if 75 then it's 30 km/hour. Given the journey is 80 km, going at 96 km/hour average seems more reasonable. x is probably 20.