Question

Malcolm and Ravi raced each other.
The average of their maximum speeds was 260\ km/h If doubled, Malcolm's maximum speed would be 80\ km/h more than Ravi's maximum speed.
What were Malcolm's and Ravi's maximum speeds?

Answer 1

Let the maximum speed of M be m and that of R be r.
A/q
2[(m+r)/2]= 260*2
=> m+r = 520
=> (80+r) +r =520 (as given in the question)
=>80+2r=520
=>2r=440
=>r=220
Then
m+220=520
=> m = 300

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Answer 2

Answer:

Recall that x denotes Malcolm's maximum speed and y denotes Ravi's maximum speed. Therefore, Malcolm's maximum speed was 200 and Ravi's maximum speed was 320

Step-by-step explanation:

Let xxx represent Malcolm's maximum speed and let yyy represent Ravi's maximum speed. Since we have two unknowns, we need two equations to find them.

Let's use the given information in order to write two equations containing xxx and yyy. For instance, we are given that the average of Malcolm's and Ravi's maximum speeds was \textit{260 km/h}260 km/hstart text, 260, space, k, m, slash, h, end text. How can we model this sentence algebraically?

Hint #22 / 4

The average of the maximum speeds is modeled by \dfrac{x+y}{2}  

2

x+y

​  

start fraction, x, plus, y, divided by, 2, end fraction. Since that average was 260\text{ km/h}260 km/h260, start text, space, k, m, slash, h, end text, we get the following equation:

\dfrac{x+ y}{2} = 260  

2

x+y

​  

=260start fraction, x, plus, y, divided by, 2, end fraction, equals, 260

Let’s multiply both sides of this equation by 222 to avoid fractions:

x+ y = 520x+y=520x, plus, y, equals, 520

We are also given that twice Malcolm's maximum speed was \textit{80 km/h}80 km/hstart text, 80, space, k, m, slash, h, end text more than Ravi's maximum speed. This can be expressed as:

2x=y+802x=y+802, x, equals, y, plus, 80

Let's rewrite this equation so that it's solved for yyy:

y = 2x-80y=2x−80y, equals, 2, x, minus, 80

Now that we have a system of two equations, we can go ahead and solve it!

Hint #33 / 4

Let's substitute \pink y=\pink{2x-80}y=2x−80start color #ff00af, y, end color #ff00af, equals, start color #ff00af, 2, x, minus, 80, end color #ff00af into the first equation:

\begin{aligned}x+ \pink y &= 520\\\\ x+(\pink{2x-80})&=520\\\\ 3x &=600\\\\ x&=200\end{aligned}  

x+y

x+(2x−80)

3x

x

​  

 

=520

=520

=600

=200

​  

 

Now we can substitute x = 200x=200x, equals, 200 into x+y=520x+y=520x, plus, y, equals, 520 and find that y=320y=320y, equals, 320.