Question

Marisol left Los Angeles at 2:30 to drive to Santa Barbara, a distance of 95 miles. The traffic was heavy until 3:20. She drove the rest of the way in very light traffic and arrived at 4:20. Her speed in heavy traffic was 40 miles an hour slower than her speed in light traffic. Find her speed in heavy and light traffic.

Answer 1

Marisol speed is 30 mph in heavy traffic and 70 mph in light traffic

Solution:

Let x be the speed in heavy traffic in miles per hour

Let y be the speed in light traffic in miles per hour

Her speed in heavy traffic was 40 miles an hour slower than her speed in light traffic

x = y - 40

y - x = 40 --------- eqn 1

Marisol left Los Angeles at 2:30 to drive to Santa Barbara, a distance of 95 miles

Therefore,

Total distance = 95 miles

Marisol left Los Angeles at 2:30

The traffic was heavy until 3:20

Therefore,

Time taken in heavy traffic = 2 : 30 to 3 : 20 = 50 minutes

$50\ minutes = \frac{50}{60}\ hour = \frac{5}{6}\ hour$

We know that,

$Distance = speed \times time$

$Distance\ traveled\ in\ heavy\ traffic = x \times \frac{5}{6} = \frac{5}{6}x$

She drove the rest of the way in very light traffic and arrived at 4:20

Time taken in light traffic = 3 : 20 to 4 : 20 = 1 hour

$Distance\ traveled\ in\ light\ traffic = y \times 1 = y$

Since, Total distance = 95 miles

$\frac{5x}{6} + y = 95\\\\5x + 6y = 95 \times 6\\\\5x + 6y = 570 ------ eqn 2$

Solve eqn 1 and eqn 2

Multiply eqn 1 by 5

5y - 5x = 200 --- eqn 3

Add eqn 2 and eqn 3

5x + 6y + 5y - 5x = 570 + 200

11y = 770

y = 70

Substitute y = 70 in eqn 1

70 - x = 40

x = 30

Thus her speed is 30 mph in heavy traffic and 70 mph in light traffic