1) A motor boat, traveling 10 miles per hour, left a marina. After three
hours, a speed boat going 30 miles per hour began to follow the motor
boat. How long did it take the speed boat to overtake the motor boat?
D(motor boat) = D(speed boat)
10(t + 3)= 30t
The answer is 1 and 1/2 hours.
2) Jerry, walking 5 miles per hour, started toward his aunt’s house 12
miles away. Thirty minutes later, his cousin Darryl started from the
aunt’s house on his bike to meet him, riding 10 miles per hour. How long
will Darryl ride before he meets Jerry?
Jerry’s Distance + Darryl’s Distance = 12 miles
5t + 10(t – ½) = 12
The answer is 38 minutes.
3) Two friends leave a hotel at the same time traveling in opposite
directions. They travel for four hours and are then 480 miles apart. If
Susan travels 10 miles per hour faster than Joan, find the average rate of
speed for each person.
Susan’s distance + Joan’s distance = 480
4(r + 10) + 4r = 480
The answer is Joan’s speed is 55 mph and Susan’s speed is 65
mph.
4) A runner decides to run out to Bristol. He begins to run at an average
rate of 9 miles per hour. He runs a certain distance and then turns
around and returns along the same route at an average rate of 6 miles
per hour. If the round trip took 2 and a half hours, how far did the
runner travel before turning around?
Distance to Bristol = Distance from Bristol
9t = 6(2.5 – t)
9t = 15 – 6t
T = 1 hour, so…
The answer is 9 miles.
5) Two students on bicycles leave their classroom building at 10:00 AM
and travel in opposite directions. If the average speed of one of the
students is 12 kilometers per hour and the average speed of the other
student is 14 kilometers per hour, at what time will they be 65
kilometers apart?
Distance 1 + Distance 2 = 65 km
12t + 14t = 65
T = 2.5 hours, so…
The answer is 12:30 P.M.
6) James leaves his home town traveling 70 miles per hour. At the same
time Paul leaves home traveling 75 miles per hour. The two live 580
miles apart and are traveling to meet each other for a lunch meeting at
noon. What time did they leave their homes?
James’ Distance + Paul’s Distance = 580
70t + 75t = 580
T = 4 hours, so…
The answer is 8 A.M.
7) Kansas city and Denver are 330 miles apart. Two cars start from
these cities traveling toward each other. They meet after 3 hours. Find
the rate of each car if one travels 20 mph slower than the other.
Distance towards KC + Distance towards Denver = 330
3r + 3(r – 20) = 330
The answer is 45 mph and 65 mph.
8) Two trains are 150 miles apart and are traveling toward each other.
If one train is going twice as fast as the other and they will meet in two
hours, how fast is the faster train going?
2r + 4r = 150
The answer is 50 mph.
9) Two cars leave town at the same time traveling in opposite
directions. One car travels at a rate of 60 miles per hour. The other car
travels at a rate of 70 miles per hour. How far apart will the two cars be
at the end of 4 hours?
Hint: Yes, this is REALLY easy! Just find the distance each one travels.
60mph times 4 hours = 240 miles
70mph times 4 hours = 280 miles
280 miles + 240 miles = 520 miles
The answer is 520 miles.
10) John’s father is 5 times older than John and John is twice as old as his
sister Alice. In two years time, the sum of their ages will be 58. How old is
John now?
Hint: Let Alice’s age = a, John’s age = 2a, dad’s age = 10a. In two years,
they will all be two years older, so add two to each “current age”.
In 2 years, Alice’s age = a + 2, John’s age = 2a + 2, dad’s age = 10a + 2.
The sum of their “future” ages is 58, so add them all together.
(a + 2) + (2a + 2) + (10a + 2) = 58
13a + 6 = 58
13a = 52
a = 4…so Alice is 4 years old.
The answer, John is currently 8.