Respuesta :
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.
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.
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 [tex]\frac{x+y}{2}=260[/tex]
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
