Solving Word Problems With Equations Of One Degree And One Unknown Worksheet With Answers Page 17
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20Solve for x. x=$3000
DISTANCE PROBLEMS
1. Two boats start from the same place on a lake but go in opposite directions.
The first boat travels at a constant speed of 15km/hr, and the second at a
constant speed of 12km/hr. How far apart are the two boats after 3 hours?
(HINT: Draw a diagram)
Let X1=distance traveled by the first boat
Let X2=distance traveled by the second boat
X1=15(3)
X2=12(3)
Total distance traveled X1+X2 = 45 + 36 = 8
2. An airplane made a trip of 680 miles in 4 hours. Part of the trip was made at 150mph
and the remainder at 180mph. How many miles were traveled at each rate? (HINT:
You have only one vehicle, but there are two parts to its journey. You also need the
‘whole-part’ hint from the end of the investment problems section for your time
column.)
Let x = number of miles traveled at 150 mph
680 – x = number of miles traveled at 180 mph
Rate
Time
distance
150
T
x= 150t
180
4-t
680-x=180(4-t)
4
680
680 = 150t + 180(4-t) solve for t.
t = 4/3 hours.
Distance traveled at 150 mph = (4/3)(150)= 200 miles traveled at 150 mph
and 680-200 = 480 miles traveled at 180 mph
3. Two friends leave two towns at the same time and start travelling toward each other
in Autos. One averages 40mph and the other 50mph. How far does each travel before
meeting if the towns are 270 miles apart?
let x = distance traveled at 40 mph x = “
“ 50 mph after t hours they meet
x = 40t x = 50t
x + x = 270 since the distance between towns is 270.
40t + 50t = 270 t = 3 hours
4. Mike can row his boat from the hunting lodge upstream to the park in 5 hours. He can
row back to the lodge in 3 hours. If the stream is flowing at 2km per hour, how fast is
Mike rowing in still water?
Let r = speed in still water
x upstream t = 5 hours
r – 2
x t=3 r + 2
17
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