Question

Malcolm and Ravi raced each other.

The average of their maximum speeds was 260\text{ km/h}260 km/h260, start text, space, k, m, slash, h, end text. If doubled, Malcolm's maximum speed would be 80\text{ km/h}80 km/h80, start text, space, k, m, slash, h, end text more than Ravi's maximum speed.
What were Malcolm's and Ravi's maximum speeds?

Answer 1

Let m and r represent the maximum speeds of Malcolm and Ravi in km/h, respectively.

... (m + r)/2 = 260 . . . . . the average of their speeds was 260 kph

... 2m = r + 80 . . . . . . . . double Malcolm's speed is 80 kph more than Ravi's

The second equation can be solved for r and that expression substituted into the first equation.

... 2m - 80 = r . . . . . . . . . . . an expression for r from the second equation

... (m + 2m - 80)/2 = 260 . . . the result of substituting that into the first

... 3m - 80 = 520 . . . . . . . . multiply by 2

... m = 200 . . . . . . . . . . . . . add 80 and divide by 3

... 2·200 - 80 = r = 320 . . .substitute the value of m into the expression for r

Malcolm's maximum speed was 200 km/h.

Ravi's maximum speed was 320 km/h.

Explanation: