SDT Practice SET – 2
Speed, Distance & Time: Level 2
1.
A person drives to work at 40 mph and returns home along the same route at 60 mph. What is the average speed for the round trip?
Solution (C):
Formula for round trip average speed: \( \frac{2xy}{x+y} \).
\( \frac{2(40)(60)}{40+60} = \frac{4800}{100} = 48 \) mph.
2.
Car A starts at 1:00 PM traveling 50 mph. Car B starts from the same place at 3:00 PM traveling 75 mph in the same direction. At what time will Car B catch Car A?
Solution (B):
Head start for A = 2 hours \(\times\) 50 mph = 100 miles.
Relative speed (same direction) = \( 75 – 50 = 25 \) mph.
Time to catch up = \( \text{Gap} / \text{Rel Speed} = 100 / 25 = 4 \) hours.
3:00 PM + 4 hours = 7:00 PM.
3.
Two cyclists are 120 miles apart. They start riding toward each other at the same time. One rides at 18 mph, the other at 22 mph. How long until they meet?
Solution (A):
Relative speed (opposite) = \( 18 + 22 = 40 \) mph.
Time = \( 120 / 40 = 3 \) hours.
4.
In \(x\) hours and \(y\) minutes, a car traveled \(z\) miles. What is the car’s speed in miles per hour?
Solution (D):
Total time in hours = \( x + y/60 = (60x + y)/60 \).
Speed = \( \text{Dist} / \text{Time} = z / [(60x+y)/60] = 60z / (60x + y) \).
5.
A man travels from home to work at 30 mph and returns at 20 mph. If the total travel time is 5 hours, what is the one-way distance?
Solution (E):
Let distance = \(d\).
\( T_{go} + T_{return} = 5 \).
\( d/30 + d/20 = 5 \).
Multiply by 60: \( 2d + 3d = 300 \implies 5d = 300 \implies d = 60 \).
6.
Runner A runs at 8 mph and Runner B at 6 mph. If they start at the same time and place but run in the same direction on a straight road, how far apart will they be after 1.5 hours?
Solution (C):
Gap increases at \( 8 – 6 = 2 \) mph.
After 1.5 hours: \( 2 \times 1.5 = 3 \) miles.
7.
A bus travels at 50 mph for 2 hours and then at 70 mph for 3 hours. What is the average speed?
Solution (B):
Dist 1 = \( 50 \times 2 = 100 \). Dist 2 = \( 70 \times 3 = 210 \). Total Dist = 310.
Total Time = 5 hours.
Avg Speed = \( 310 / 5 = 62 \) mph.
8.
If a cyclist travels 15 miles in 2 hours, what is his rate in miles per minute?
Solution (A):
Rate = \( 15 \text{ miles} / 120 \text{ minutes} \).
\( 15/120 = 1/8 \) miles/min.
9.
A train moving at 60 mph passes a standing person in 3 seconds. What is the length of the train in feet? (1 mile = 5280 feet)
Solution (D):
60 mph = \( 60 \times 5280 \text{ ft} / 3600 \text{ sec} = 88 \) ft/sec.
Distance = Rate \(\times\) Time = \( 88 \times 3 = 264 \) feet.
10.
A boat goes 15 mph in still water. The current flows at 5 mph. How long does it take to travel 40 miles downstream?
Solution (C):
Downstream Speed = Boat + Current = \( 15 + 5 = 20 \) mph.
Time = \( 40 / 20 = 2 \) hours.
Score: 0 / 0