Question

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?

Answer 1

Answer:

Maximum speed of Malcolm = 200 KM/hour

Maximum speed of Robby = 320 Km/hour

Step-by-step explanation:

To solve this question we will form the equations as per statements given in the question.

Let the maximum speed of Malcolm is x KM/hour and Robbie's maximum speed be y KM/hour.

Now it given that average of maximum speeds of both is 260 KM/hour

So the equation will be $\frac{x+y}{2}=260$

x + y = 260×2 = 520 ------(1)

It is given that if doubled Malcolm's maximum speed would be 80 KM/hour more than Robby's maximum speed.

2x = y + 80

2x - y = 80 --------(2)

Now we add equation 1 to equation 2

(x + y) + (2x - y) = 520 + 80

3x = 600

x = 200 KM/hour

Finally we put the value of x in equation 1

200 + y = 520

y = 520 - 200 = 320 KM/hour

Finally the answer is maximum speed of Malcolm is 200 KM/hour and maximum speed of Robby is 320 KM/hour

Answer 2

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:
$\frac{(\frac{R}{2}+40)+R}{2}=260$

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

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:
$\frac{R}{2}+40+\frac{2R}{2}=520 \\ \\\frac{3R}{2}+40=520$

Subtract 40 from both sides:
$\frac{3R}{2}+40-40=520-40 \\ \\\frac{3R}{2}=480$

Now we will multiply both sides by 2:
$\frac{3R}{2}\times 2=480\times 2 \\ \\3R=960$

Divide both sides by 3:
$\frac{3R}{3}=\frac{960}{3} \\ \\R=320$

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