Question

At noon, Bradley began steadily increasing the

speed of his car by 2 miles per hour every minute. At 12:15 p.m., he realized he was going
15 miles per hour over the speed limit. If his speed at noon was 40 miles per hour, what was the speed limit at 12:15 p.m.?

Please show work step by step

Answer 1

25.5 mph

Explanation:

Given information:

• Bradley increases the speed of his car by 2 miles per hour.
• 12.00 pm: Bradley's speed = 40 mph
• 12.15 pm: Bradley is driving at 15 miles over the speed limit.

Calculate Bradley's speed at 12.15 pm:

60 minutes = 1 hour

⇒ 15 minutes = 1/4 hour

⇒ speed at 12.15 pm = speed at 12.00pm + 1/4 of 2 mph

= 40 mph + 0.5 mph

= 40.5 mph

If he was 15 miles over the speed limit at 12.15 pm then:

⇒ speed limit = speed at 12.15pm - miles over the limit

= 40.5 mph - 15

= 25.5 mph

Therefore, the speed limit was 25.5 mph.

Answer 2

25.5 mph

Explanation:

So Bradley's speed can be modeled by the equation y=2x+40 where y=speed, x=time in hours after noon, and b=initial speed

So 12:15 is 15 minutes after noon, which is also 0.25 or 1/4 of an hour after noon. This is the x-value. Plug this into the equation to get his speed at 12:15

y=2(0.25)+40

y=0.5+40

y=40.5

So his speed was 40.5 at the time and since he was going 15 miles over the speed limit, the speed limit is 15 less than his speed

40.5 - 15 = 25.5