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

Answer:

Step-by-step 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 = $\frac{5}{6}$ hour

We know that $Distance=speed\times time$

Distance traveled in heavy traffic = $d_1=\frac{5}{6}x$

Time taken in light traffic = 1 hour

Distance traveled in light traffic = $d_2=1\times y=y$

Since, Total distance = 95 miles

$\Rightarrow\ d_1+d_2=95\\\Rightarrow\frac{5}{6}x+y=95\\\Rightarrow\ 5x+6y=570..........(1)$

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.

Answer 2

Answer:

30 mph in heavy traffic, 70 mph in light traffic

Step-by-step explanation: