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 40 miles per hour slower than her speed in light traffic. Find her speed in heavy traffic and in light traffic

Answer 1

30 mph in heavy traffic, 70 mph in light traffic

Explanation:

Answer 2

Explanation:

Let x be the speed in heavy traffic and y be the speed in light traffic in miles per hour.

Total distance = 95 miles

Time taken in heavy traffic = 50 minutes =
`(5)/(6)` hour

We know that
`Distance=speed* time`

Distance traveled in heavy traffic =
`d_1=(5)/(6)x`

Time taken in light traffic = 1 hour

Distance traveled in light traffic =
`d_2=1* y=y`

Since, Total distance = 95 miles

`\Rightarrow\ d_1+d_2=95\\\Rightarrow(5)/(6)x+y=95\\\Rightarrow\ 5x+6y=570..........(1)`

Also, Her speed in heavy traffic 40 miles per hour slower than her speed in light traffic.

`\Rightarrow\ y-x=40.............(2)`

Multiply this equation by 5 on both sides, we get

`5y-5x=200..................(3)`

Add (3) and (1), we get (5x will be cancelled)

`11y=770\\\Rightarrow\ y=70`

From equation, (2), we get

`70-x=40\\\Rightarrow\ x=30`

Hence, Her speed in heavy traffic is 30 miles per hour and in light traffic is 30 miles per hour.