Question # Adventure Tours has 6 leisure-tour trolleys that travel 15 mph slower than their 3 express tour buses. The bus travels 132 mi in the time it takes the trolley to travel 99 mi. Find the speed of each mode of transportation.

Ratios, rates, proportions
ANSWERED Adventure Tours has 6 leisure-tour trolleys that travel 15 mph slower than their 3 express tour buses. The bus travels 132 mi in the time it takes the trolley to travel 99 mi. Find the speed of each mode of transportation. 2021-02-01

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. 2021-08-10

Answer is given below (on video)