Bunuel wrote:

Official Solution:

A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling, what was her average speed on the second day?

A. 5 mph

B. 10 mph

C. 20 mph

D. 30 mph

E. 40 mph

Approach 1 - Algebra:

Since on the second day the cyclist traveled 4 hours longer than she traveled on the first day and spent a total of 12 hours traveling then \(t+(t+4)=12\), so \(t=4\). So, she traveled 4 hours on the first day and 8 hours on the second day;

Let the rate on the second day be \(r\) mile per hour, then: \(4(r+10)+8r=280\), so \(r=20\).

Instead, let the rate on the first day be r mile per hour, the rate on the second day be (r-10), then

\(4(r) + 8(r-10) = 280\), so \(r=30\). What's the wrong with this approach?