Chris B. answered • 07/12/16
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48) At 10:00 A.M. two classmates start out on their bikes to meet each other from towns located 68 miles apart. At 1:00 P.M. they meet. If one boy traveled 3 miles per hour faster than the other, what was the rate of speed of each boy?
Speed is distance per unit time so we'll use miles per hour (mph) for these.
The slower boy's speed is unknown so we use the variable x.
slower speed= x
faster speed= x + 3
The total time is 3 hrs for each boy, but the total distance is 68 mi.
To find out the distance for each boy, you must multiply the 3 hours (time) and speed together. speed = distance/time so distance = time*speed
slower distance = 3x
faster distance = 3(x +3)
Then you can add them together to equal the total distance. Solve for slow speed(x).
3x + 3(x + 3) = 68
3x + 3x + 3*3 = 68 distribute
6x + 9 = 68 add like terms
6x = 68 - 9 isolate term with variable
6x = 59
x = 59/6 = 9 5/6 mph (slow speed)
x + 3 = 12 5/6 mph (faster speed)
Check:
slower distance = 3x = 3*(9 5/6) = 59/2 = 29.5 mi.
faster distance = 3(12 5/6) = 77/2 = 38.5 mi.
29.5 mi. + 38.5 mi. = 68 mi.
Final answer: Slower boy went 9 5/6 mph and the faster boy went 12 5/6 mph.
(Make sure that the numbers from the problem were copied correctly. Your answer is not an integer here like 49 is.)
49) At 12:00 noon two Mississippi steam boats are 126 miles apart. At 6:00 P.M. they pass each other going in opposite directions. If one steamboat travels 9 miles per hour faster than the other, find the speed of both boats.
Time for each is 6 hours.
Total distance for both together is 126 mi.
slower speed = x
faster speed = x + 9
Multiply each speed by 6 hrs to find distance for each.
slower distance = 6x
faster distance = 6(x + 9)
Add distances to create an equation in terms of x.
6x + 6(x + 9) = 126
6x + 6x + 6*9 = 126 distribute
12x + 54 = 126 add like terms
12x = 126 - 54 isolate term with variable
12x = 72
x = 6 mph (slower speed)
x + 9 = 6 + 9 = 15 mph (faster speed)
Check:
Use x to find each boat's distance.
slower distance = 6 hr * 6 mph = 36 mi
faster distance = 6 hr * 15 mph = 90 mi
36 mi. + 90 mi. = 126 mi.
Final answer: slower boat speed is 6 mph and faster boat speed is 15 mph.
Speed is distance per unit time so we'll use miles per hour (mph) for these.
The slower boy's speed is unknown so we use the variable x.
slower speed= x
faster speed= x + 3
The total time is 3 hrs for each boy, but the total distance is 68 mi.
To find out the distance for each boy, you must multiply the 3 hours (time) and speed together. speed = distance/time so distance = time*speed
slower distance = 3x
faster distance = 3(x +3)
Then you can add them together to equal the total distance. Solve for slow speed(x).
3x + 3(x + 3) = 68
3x + 3x + 3*3 = 68 distribute
6x + 9 = 68 add like terms
6x = 68 - 9 isolate term with variable
6x = 59
x = 59/6 = 9 5/6 mph (slow speed)
x + 3 = 12 5/6 mph (faster speed)
Check:
slower distance = 3x = 3*(9 5/6) = 59/2 = 29.5 mi.
faster distance = 3(12 5/6) = 77/2 = 38.5 mi.
29.5 mi. + 38.5 mi. = 68 mi.
Final answer: Slower boy went 9 5/6 mph and the faster boy went 12 5/6 mph.
(Make sure that the numbers from the problem were copied correctly. Your answer is not an integer here like 49 is.)
49) At 12:00 noon two Mississippi steam boats are 126 miles apart. At 6:00 P.M. they pass each other going in opposite directions. If one steamboat travels 9 miles per hour faster than the other, find the speed of both boats.
Time for each is 6 hours.
Total distance for both together is 126 mi.
slower speed = x
faster speed = x + 9
Multiply each speed by 6 hrs to find distance for each.
slower distance = 6x
faster distance = 6(x + 9)
Add distances to create an equation in terms of x.
6x + 6(x + 9) = 126
6x + 6x + 6*9 = 126 distribute
12x + 54 = 126 add like terms
12x = 126 - 54 isolate term with variable
12x = 72
x = 6 mph (slower speed)
x + 9 = 6 + 9 = 15 mph (faster speed)
Check:
Use x to find each boat's distance.
slower distance = 6 hr * 6 mph = 36 mi
faster distance = 6 hr * 15 mph = 90 mi
36 mi. + 90 mi. = 126 mi.
Final answer: slower boat speed is 6 mph and faster boat speed is 15 mph.
