Malcolm and Robbie raced each other. The average of the maximum speed was 260 KM/hour. if doubled Malcolm’s maximum speed would be 80 KM/hour more than Robbys maximum speed. what were Malcolm’s and Robbie‘s maximum speed?

The correct answers are:

Malcolm's maximum speed is 200 km/hr and Robbie's is 320 km/hr.

Explanation:

Let R be Robbie's maximum speed and M be Malcolm's maximum speed. If Malcolm's speed is doubled (2M), it is 80 more than Robbie's (R+80); this gives us the equation
2M = R + 80.

We can isolate M by dividing both sides by 2:
2M/2 = R/2 + 80/2
M=R/2+40.

We know that their average is 260 km/hr. The average is found by adding the two maximum speeds together and dividing by 2:
(M+R)/2=260.

We will substitute our value for M from above:
[tex]\frac{(\frac{R}{2}+40)+R}{2}=260[/tex]

To solve this, we can multiply both sides by 2:
[tex]\frac{(\frac{R}{2}+40)+R}{2}\times 2=260\times 2 \\ \\\frac{R}{2}+40+R=520[/tex]

We can combine like terms, but to do that, we must write R as a fraction over 2. Since it is 1R, this is 2R/2:
[tex]\frac{R}{2}+40+\frac{2R}{2}=520 \\ \\\frac{3R}{2}+40=520[/tex]

Subtract 40 from both sides:
[tex]\frac{3R}{2}+40-40=520-40 \\ \\\frac{3R}{2}=480[/tex]

Now we will multiply both sides by 2:
[tex]\frac{3R}{2}\times 2=480\times 2 \\ \\3R=960[/tex]

Divide both sides by 3:
[tex]\frac{3R}{3}=\frac{960}{3} \\ \\R=320[/tex]

Plugging this into our first equation for M, we have:
M = R/2+40
M = 320/2+40
M = 160+40
M=200.