gmatt1476 wrote:
Khalil drove 120 kilometers in a certain amount of time. What was his average speed, in kilometers per hour, during this time?
(1) If Khalil had driven at an average speed that was 5 kilometers per hour faster, his driving time would have been reduced by 20 minutes.
(2) If Khalil had driven at an average speed that was 25% faster, his driving time would have been reduced by 20%.
DS01951.01
We know that the distance is 120. Let r be his average speed. The original question: r=?
1) At the old speed, his driving time is 120/r. At the new speed, his driving time would be 120/(r+5). We can set up an equation about his new driving time, which is 1/3 hour less than his old driving time.
\(\frac{120}{r+5}=\frac{120}{r}-\frac{1}{3}\)
\(360r=360r+1800-r^2-5r\)
\(r^2+5r-1800=0\)
Since c/a is negative for the quadratic equation above, its two roots have different signs. However, only its positive root applies to the context of the problem.
Thus, we could get a unique value to answer the original question. \(\implies\)
Sufficient2) At his new speed, his driving time would be 120/(1.25r). We can set up an equation about his new driving time, which is 20% less than his old driving time.
\(\frac{120}{\frac{5}{4}r}=\frac{4}{5}\cdot \frac{120}{r}\)
The above equation is an identity. Since r can be any positive number, we can't get a unique value to answer the original question. \(\implies\)
InsufficientAnswer: A
My question is specifically around this statement. What happens in other cases(If C/A is positive etc). I am aware of discriminant properties but not heard of this before. Can you please help. This will save a lot of time as I tried to solve the quadric because I wasn't aware of this rule. Do we have any post around this?
"Since c/a is negative for the quadratic equation above, its two roots have different signs. However, only its positive root applies to the context of the problem."