On Wednesday you drove from home to work at 50 mph and got there in 43 minutes. On Thursday you drove at 68 mph. Round answers to nearest 10th. Use:
R
1
T
1
=
R
2
T
2
(double click this to see clearer)
Round to the nearest 10th and Use Unit Abbreviations for Units.
How long does the trip take on Thursday?How much time did you save by driving 18 mph faster?
Wed.: d = r*t1 = 50mi/h * (43/60)h = 35.83 mi.
Thu.: t2 = d/r = 35.83/68 = 0.527 h. = 31.6 min.
t1-t2 = 43-31.6 = 11.4 min = Time saved.
To find the time it takes to complete the trip on Thursday, we can use the formula:
Time = Distance / Rate
Since the distance traveled remains the same, we can set up the equation as follows:
R1 * T1 = R2 * T2
R1 = Rate on Wednesday = 50 mph
T1 = Time on Wednesday = 43 minutes
R2 = Rate on Thursday = 68 mph
T2 = Time on Thursday (what we're trying to find)
Now, let's substitute the known values into the equation:
50 mph * 43 minutes = 68 mph * T2
To simplify the equation, we need to convert the time from minutes to hours:
43 minutes / 60 minutes/hour = 0.72 hours
Now we have:
50 mph * 0.72 hours = 68 mph * T2
To solve for T2 (time on Thursday), divide both sides of the equation by 68 mph:
(50 mph * 0.72 hours) / 68 mph = T2
Now, calculate:
(36 mph * 0.72 hours) / 68 mph = T2
T2 ≈ 0.38 hours (rounded to the nearest 10th)
To convert hours to minutes, multiply by 60:
0.38 hours * 60 minutes/hour ≈ 23 minutes (rounded to the nearest 10th)
So, the trip on Thursday takes approximately 23 minutes (rounded to the nearest 10th).
To find how much time you saved by driving 18 mph faster, we can subtract the time on Thursday from the time on Wednesday:
Time saved = Time on Wednesday - Time on Thursday
Time saved = 43 minutes - 23 minutes
Time saved ≈ 20 minutes (rounded to the nearest 10th)
Therefore, by driving 18 mph faster, you saved approximately 20 minutes (rounded to the nearest 10th).