Question

Mike takes 20 minutes longer than Erica does to make the 462-mile drive between two cities. Erica drives 3 miles an hour faster. How fast do Mike and Erica drive?

Answer 1

Answer with explanation:

Let speed of Mike =x miles an hour

Then, Speed of Erica=(x+3) miles an hour

Total Distance between two cities which needs to get traveled by Mike and Erica=462 mile

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\\ \frac{462}{x}-\frac{462}{x+3}=\frac{20}{60}\\\\462 \times 3\times (x+3-x)= x \times (x+3)\\\\x^2+3x=4158\\\\x^2+3x-4158=0\\\\x^2+66x-63x-4158=0\\\\x*(x+66)-63*(x+66)=0\\\\(x-63)(x+66)=0\\\\x\neq -66{\text{speed can't be negative}}\\\\x=63$

Speed of Mike=63 miles an hour

Speed of Erica=63+3=66 miles an hour