CEMC Cayley, 2015

Algebra Difficulty 2.6 Junior Find the answer Canada

For the first 30 minutes of a trip, Deanna drove at a constant speed. For the next 30 minutes, she drove at a constant speed 20 km/h faster than her original speed. If the total distance that she travelled was 100 km, how fast did she drive for the first 30 minutes?

Pick one

Solution

Suppose that Deanna drove at $v$ km/h for the first 30 minutes.

Since 30 minutes equals one-half of an hour, then in these 30 minutes, she drove $\frac{1}{2}v$ km.

In the second 30 minutes, she drove at $(v+20)$ km/h.

Thus, in these second 30 minutes, she drove $\frac{1}{2}(v+20)$ km.

Since she drove 100 km in total, then $\frac{1}{2}v + \frac{1}{2}(v+20) = 100$ or $\frac{1}{2}v + \frac{1}{2}v + 10 = 100$ .

Thus, $v + 10 = 100$ or $v=90$ .

Therefore, Deanna drove 90 km/h for the first 30 minutes.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.