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 = [tex]\frac{5}{6}[/tex] hour
We know that [tex]Distance=speed\times time[/tex]
Distance traveled in heavy traffic = [tex]d_1=\frac{5}{6}x[/tex]
Time taken in light traffic = 1 hour
Distance traveled in light traffic = [tex]d_2=1\times y=y[/tex]
Since, Total distance = 95 miles
[tex]\Rightarrow\ d_1+d_2=95\\\Rightarrow\frac{5}{6}x+y=95\\\Rightarrow\ 5x+6y=570..........(1)[/tex]
Also, Her speed in heavy traffic 40 miles per hour slower than her speed in light traffic.
[tex]\Rightarrow\ y-x=40.............(2)[/tex]
Multiply this equation by 5 on both sides, we get
[tex]5y-5x=200..................(3)[/tex]
Add (3) and (1), we get (5x will be cancelled)
[tex]11y=770\\\Rightarrow\ y=70[/tex]
From equation, (2), we get
[tex]70-x=40\\\Rightarrow\ x=30[/tex]
Hence, Her speed in heavy traffic is 30 miles per hour and in light traffic is 30 miles per hour.
Answer:
30 mph in heavy traffic, 70 mph in light traffic
Step-by-step explanation:
