Question

a. find the distance around the park to the nearest yard.
the distance is about 101 yards

b. a new path and a bridge are constructed from point q to the mid - point m of (overline{pr}). find qm to the nearest yard.
qm≈40 yd

c. a man jogs from p to q to m to r to q and back to p at an average speed of 150 yards per minute. to the nearest tenth of a minute about how long does it take him to travel the entire distance?
it takes about minutes.

Explanation:

Step1: Determine total distance

The man jogs from \(P\) to \(Q\) to \(M\) to \(R\) to \(Q\) and back to \(P\). We know from part a that the perimeter (distance around the park) is about \(101\) yards and from part b \(QM\approx40\) yards. The total distance \(d\) he jogs is the perimeter of the park plus \(2\times QM\) (since he goes through \(QM\) twice). So \(d = 101+2\times40=101 + 80=181\) yards.

Step2: Use speed - time formula

The speed - time formula is \(t=\frac{d}{s}\), where \(t\) is time, \(d\) is distance and \(s\) is speed. Given \(s = 150\) yards per minute and \(d = 181\) yards. Then \(t=\frac{181}{150}\approx1.2\) minutes.

Answer:

\(1.2\)