Question

Mike runs in lane one around a curve, while Maurice runs in lane eight around a curve. The radius of lane eight is twice as big as the radius of lane one. If Mike has to run 50 m to get fully around the curve in lane one, how far does Maurice have to run to get fully around the curve in lane eight? Group of answer choices a.150 m b. 50 m c.25 m d.100 m

Answer 1

D. 100m

Explanation:

From the question, we know that there are 2 lanes lane 1 and lane 8.

The relationship between both is that lane 8 has a radius twice that of lane 1 which we do not know the actual values. Hence, if we say the radius of lane 1 is r, the radius of lane 8 will be 2r.

We also know that Mike has to run 50m to get fully around the curve in lane 1. This tells us that the length along the boundary of lane 1 is 50m I.e it has a circumference of 50m.

The formula for circumference of a circle is 2πr. Hence, 2πr = 50 for lane 1. Using mathematical manipulations, π = 50/2r

Now for lane 8, we have a bigger radius twice in length and which we represented by 2r.

The length of lane 8 curve is also 2πr.

now, our π from lane 1 above is 50/2r. We then substitute this value.

2 × 50/2r × 2r = 100m