Answer:
1:30pm
Step-by-step explanation:
Start Time: 10:00am
Start Speed: 40MPH
Time for Lunch: 30minutes
Arrival Time: 5:00pm
Ending Speed: 50MPH
Total Miles: 290miles
Find Total Time Taken:
5pm - 10am = 7 hours
7 hours - 30 minutes (lunch) = 6.5 hours of travel
Create Equations:
Distance = Speed x Time
Finding Total Numbers of Miles Traveled
Miles = SpeedBefore x TimeBefore + SpeedAfter x TimeAfter
290(Miles) = 40(mph) x E + 50(mph) x Y
290 = 40E + 50A
Finding Time Traveled Before and After the lunch break
Note: It is based on duration in hours
Total Time = Time Before + Time After + Lunch Time
7 hours = E + Y + .5 hours
7 = E + Y + .5
Solve for Y
7 = Y + E + .5
6.5 = Y + E
6.5 - E = Y
Use Substitution in second equation to solve for E
290 = 40E + 50Y
290 = 40E + 50(6.5 - E)
290 = 40E + (325 - 50E)
290 = 40E + 325 - 50E
290 = -10E + 325
-35 = -10E
10E = 35
E = 3.5 hours, time traveled before lunch
Note: The following is unnecessary
Solve for Y, Again
Y = 6.5 - E
Y = 6.5 - 3.5
Y = 3 hours, time traveled after lunch
So the man traveled for 3.5 hours and then ate lunch. Then he traveled for 3 more hours.
So...
10am + 3.5 hours = 1:30pm - the time when he ate lunch
