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.

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

We know that,

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

Since, Total distance = 95 miles

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

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