Question 192637: Ruth was hauling a wide load out of Boston. At 4:00 a.m. she headed south from exit 129 at an average of 25 mph. Nadia headed south from the same exit at 11:00 a.m. in her Toyota. By 5:00 p.m. the same day Nadia was 17 miles ahead of Ruth. what was Nadia's average speed?
Okay, so I have NO idea how to do this. what times do I use? My teacher has my class use the whole D=RT formula, but since there are two people and one is ahead of the other how do I work this out?
Please and thank you,
Christina
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! Ruth was hauling a wide load out of Boston. At 4:00 a.m. she headed south from exit 129 at an average of 25 mph. Nadia headed south from the same exit at 11:00 a.m. in her Toyota. By 5:00 p.m. the same day Nadia was 17 miles ahead of Ruth. what was Nadia's average speed?
Make this chart.
D R T
Ruth
Nadia
We want to know Nadia's speed, so we put x for
Nadia's rate (speed):
D R T
Ruth
Nadia x
>>...Ruth...headed south...at an average of 25 mph.
So we put 25 for Ruth's speed
D R T
Ruth 25
Nadia x
Ruth traveled from 4 AM to 5 PM, which is 13
hours. So we put 13 for Ruth's time
D R T
Ruth 25 13
Nadia x
Now we use D=RT to get Ruth's total distance at 5PM.
D = (25)(13) = 325 miles, so we put 325 for Ruth's
distance
D R T
Ruth 325 25 11
Nadia x
Nadia traveled from 11 AM to 5 PM, so her time was 6 hours.
So we put 6 for Nadia's time.
D R T
Ruth 325 25 11
Nadia x 6
Now we use D=RT to get Nadia's total distance at 5PM.
D = (x)(6) = 6x miles, so we put 6x for Nadia's
distance
D R T
Ruth 325 25 11
Nadia 6x x 6
Now that the chart is complete, we make the equation from
what we didn't use to make the chart. That was this:
>>...By 5:00 p.m. the same day Nadia was 17 miles ahead of Ruth...<<
So Nadia's distance = Ruth's distance + 17, so
6x = 325 + 17
6x = 342
Divide both sides by 6
x = 57 mph
Edwin
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