Multiple choice

Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

  1. 150

  2. 100

  3. 90

  4. 120
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be v1 and v2. (v1+v2) * 1.5 = D. (v1-v2) * 10.5 = D. 1.5(v1+v2) = 10.5(v1-v2). v1+v2 = 7(v1-v2). v1+v2 = 7v1-7v2. 8v2 = 6v1. v1 = 4/3 * v2. If v2=60, v1=80. D = (80+60)*1.5 = 140*1.5 = 210. Distance by slower car = 60 * 1.5 = 90.

AI explanation

Using the formula Time equals Distance divided by Relative Speed, the total distance between the starting points is 1.5 times the sum of their speeds and also 10.5 times the difference of their speeds. Equating these gives 1.5 times the sum equals 10.5 times the difference, which simplifies to the sum of their speeds being seven times their difference. With the slower car's speed at 60 km/hr, substituting this into the equation yields a faster car speed of 80 km/hr, making the total distance 1.5 multiplied by 140, which equals 210 km. When traveling towards each other, the slower car travels for 1.5 hours at 60 km/hr, covering a distance of 90 km. The result is 90.

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