Problem 1 :
If a person travels at a rate of 40 miles per hour. At the same rate, how long will he take to cover 160 miles distance?
Problem 2 :
A person travels at a rate of 60 km per hour. Then how many meters can he travel in 5 minutes?
Problem 3 :
Bicyclists Bryan and Jack started at noon from points 60 km apart and rode toward each other, meeting at 1:30 p.m. Bryan's speed was 4 km/h greater than Jack's speed. Find their speeds.
Problem 4 :
A helicopter leaves Airport and flies north at 180 mi/h. Twenty minutes later a plane leaves the same airport and follows the helicopter at 330 mi/h. How long does it take the plane to overtake the helicopter?
Problem 5 :
A ski lift carried up a slope at the rate of 6 km/h. and she skied back down parallel to the lift at 34 km/h. The round trip took 30 min. How far did she ski and for how long?
1. Answer :
Given : Rate is 40 miles per hour.
The formula to find the time when distance and rate are given is
Time = Distance/Rate
Time taken to cover the distance of 160 miles is
Time = 160/40
Time = 4 hours
So, the person will take 4 hours to cover 160 miles distance at the rate of 40 miles per hour.
2. Answer :
Given : Rate is 60 km per hour.
The distance covered in 1 hour or 60 minutes is
= 60 km
= 60 ⋅ 1000 meters
= 60000 meters
Then the distance covered in 1 minute is
= 60000/60
= 1000 m
The distance covered in 5 minutes is
= 5 ⋅ 1000
= 5000 meters
So, the person can cover 5000 meters distance in 5 minutes.
3. Answer :
Step 1 :
Begin with drawing a sketch.
Step 2 :
Let r = Jack's speed.
Then, Bryan's speed = (r + 4).
Both started at noon (12:00 p.m.) and meeting each other at 1 : 30 p.m.
So, both of them take 1.5 hours time to meet each other from their starting points.
Prepare a chart organizing the given facts and use it to label the sketch.
Step 3 :
Based on the sketch and information in step 2, we can form equation as shown below.
1.5(r + 4) + 1.5r = 60
Step 4 :
Solve the equation in step 3 for r.
1.5(r + 4) + 1.5r = 60
Simplify.
1.5r + 6 + 1.5r = 60
3r + 6 = 60
Subtract 6 from each side.
3r = 54
Divide each side by 3.
r = 18
r + 4 = 18 + 4 = 22
So, Jack's speed is 18 km/hr. and Bryan speed is 22 km/hr.
4. Answer :
Step 1 :
Begin with drawing a sketch.
Step 2 :
Let t = plane's flying time.
Because the speeds are given in miles per hour, we have to write 20 minutes as 1/3 hours.
Then, helicopter's flying time = (t + 1/3).
Prepare a chart organizing the given facts and use it to label the sketch.
Step 3 :
At the point where the plane overtakes the helicopter, the distance covered by the plane and helicopter will be equal.
Using distance formula, we have
330t = 80(t + 1/3)
Step 4 :
Solve the equation in step 3 for t.
330t = 180(t + 1/3)
Simplify.
330t = 180t + 60
Subtract 180t from each side.
150t = 60
Divide each side by 150.
t = 60/150
t = 2/5 hours
t = 2/5 ⋅ 60 minutes
t = 24 minutes
So, the plane overtakes the helicopter in 24 minutes.
5. Answer :
Step 1 :
Begin with drawing a sketch.
Step 2 :
Let t = Lily's skiing time.
Because the speeds are given in miles per hour, we have to write 30 minutes as 1/2 or 0.5 hours.
Step 3 :
In a round-trip, the two distances covered are equal.
Using distance formula, we have
34t = 6(0.5 - t)
Step 4 :
Solve the equation in step 3 for t.
34t = 6(0.5 - t)
Simplify.
34t = 3 - 6t
Add 6t to each side.
40t = 3
Divide both sides by 40.
t = 3/40
t = 0.075 hours
t = 0.075 ⋅ 60 minutes
t = 4.5 minutes
Distance covered :
= Rate ⋅ Time
Substitute, Rate = 34 and Time = 0.075
= 34 ⋅ 0.075
= 2.55 km
So, Maria skied for 0.075 h. or 4.5 min. for a distance of 2.55 km.
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