For motion problems, use the distance formula: distance=rate\(\times\)time\(\displaystyle\to{d}={r}{t}\)

Let x be the speed of a bus so that x-5 is the speed of the trolley, both in mph.

The time it takes for the bus to travel 132 miles is the same as the time it takes for the trolley to travel 99 miles:

\(tB=tT\)

\(\displaystyle{\left({d}\frac{{B}}{{r}}{B}\right)}={\left({d}\frac{{T}}{{r}}{T}\right)}\)

\(\displaystyle\frac{{132}}{{x}}=\frac{{99}}{{{x}-{15}}}\)

Solve for x. Cross multiply: \(132(x-15)=99x\)

\(132x-1980=99x\)

\(132x=99x+1980\)

\(33x=1980\)

\(x=60\)

So, the speed of the bus is 60 mph and the speed of the trolley is \(60-15=45\) mph.