Math word problem: find the speed of the car.

Question

At the same time, two cyclists started riding in the same direction and after an hour a car started too. The speed of the first cyclist is 24 km/h and the speed of the second cyclist is 18 km/h. The car with constant speed caught the second cyclist 10 minutes earlier than the first cyclist.

Find the speed of the car.

Answer 1

Let v is speed of car. Then, vt = 18(t + 1) and v(t + 1/6) = 24(t + 7/6)

t/(t + 1/(t + 1/6) = 3(t + 1)/[4(t + 7/6)]; 4t(t + 7/6) = 3(t + 1/6)(t + 1); 4t² + 14t/3 = 3t² +7t/2 + 1/2;

t² + 7t/6 - 1/2 = 0; 6t² + 7t - 3 = 0; t = (- 7 + √(49 + 72)/12; t = (- 7 + 11)/12 = 1/3 h

So, v·1/3 = 18·(1 + 1/3); v = 72 km/h

Answer 2

Yelfim's answer is correct.

see it this way

vt=18+18*t ,,,, bicycle going 18km/hr had hour start and after t time they are at equal distance

and

v(t+1/6)=24+24(t+1/6),,,,,, bicycle going 24km/hr had hour start and after t+1/6 tjime they are at equal sdistance.

since v=(18+18t)/t substitute that into second equation and solve for t.,,,quadratic 6t²+7x-3=0. Only positive t is valid. plug back t into either equation to find v.