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?
Malcolm's maximum speed was
km/h and Ravi's maximum speed was
km/h.

The problem can be represented by two equations:

The average of the two speeds are 260 km/hr.  ->   1/2(X + Y) = 260

Twice Malcom's speeds is 80 more than Ravi's speed -> 2X - Y = 80

where X = Malcom's maximum speed, Y = Ravi's maximum speed.

This is two equations in two unknowns:

1)X + Y = 520

2)2X - Y = 80

add equations 1 and 2

3X = 600

X = 200,

Plug X back into equation 1.

200 + Y = 520 -> Y = 320.

Malcom's maximum speed is 200 km/hr.

Ravi's maximum speed is 320 km/hr.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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