Bunuel wrote:

If a car had traveled 20 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 60 km, at what speed did it travel?

A. 35 kmh

B. 40 kmh

C. 50 kmh

D. 60 kmh

E. 65 kmh

Using answer choices, it is much easier if you use 30 minutes = \(\frac{1}{2}\) hour

Start with Answer C to get a benchmark

If original speed was 50, then time, t = D/r:

Time at 50 mph: \(\frac{60}{50}=\frac{6}{5}\) hours

20 mph faster? (50 + 20) = 70 mph. t = D/r

Time at 70 mph: \(\frac{60}{70}=\frac{6}{7}\) hours

That hour fraction in minutes will not yield an integer (30 minutes), but find the difference in times to get a benchmark

\((\frac{6}{5} - \frac{6}{7})=\frac{(42-30)}{35}=\frac{12}{35}\) hours

\(\frac{12}{35}\approx{\frac{1}{3}}\) hour

\(\frac{1}{3} < \frac{1}{2}\) hr

We need time to be longer. That means speed must be slower (decreased speed = increased travel time). Eliminate answers D and E.

Try B) 40

Time at 40 mph: \(\frac{60}{40} = \frac{3}{2}\) hour

20 mph faster: (40 + 20) = 60 mph

Time at 60 mph: \(\frac{60}{60}=1\) hour

Time difference? \(\frac{3}{2} - 1 = \frac{1}{2}\) hour = 30 minutes

Answer B

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