# Math Help - Could someone check my answers pls.

1. ## Could someone check my answers pls.

The rails on a railroad are built from thirty- foot sections. When a train wheel passes over the junction between two sections, there is an audible click. Inside a train that is traveling at 70mph, how many clicks will a passenger hear each twenty seconds?

30 clicks

In attempting to calculate the carrying capacity of a cylindrical pipe, Avery measured the outer diameter to be 2 inches, neglecting to notice that the pipe was one eighth of an inch thick. By what percent did Avery overestimate the carrying capacity of the pipe?

24%

Thanks.

Vicky.

2. Hello Vicky
Originally Posted by Vicky1997
The rails on a railroad are built from thirty- foot sections. When a train wheel passes over the junction between two sections, there is an audible click. Inside a train that is traveling at 70mph, how many clicks will a passenger hear each twenty seconds?

30 clicks

70 mph = $\frac{70 \times 5280}{3600}$ feet per sec

So in 20 sec the train passes over $\frac{70 \times 5280\times 20}{3600\times 30}$ thirty-foot sections, which is a bit more than 68.

In attempting to calculate the carrying capacity of a cylindrical pipe, Avery measured the outer diameter to be 2 inches, neglecting to notice that the pipe was one eighth of an inch thick. By what percent did Avery overestimate the carrying capacity of the pipe?

24%

Thanks.

Vicky.
I make it just over 30%.

The inner diameter is $1\tfrac34 = 1.75$ inches. The carrying capacity is proportional to the area of the cross-section, which in turn is proportional to the square of the diameter. So by using 2 in instead of 1.75 in, the area is overestimated in the ratio $2^2:1.75^2$, or by a factor of $\frac{2^2}{1.75^2}= 1.306 = 1 + 0.306$ (3 d.p.)

So Avery has overestimated by about 30.6%