SOLUTION: A cyclist traveled at a rate of 24 mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby t

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Question 102989: A cyclist traveled at a rate of 24 mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town.
d=rt
d=(24-18)4.9
d=(6)4.9
d=29.4
I'm concern whether or not my answer is correct.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If you're concerned, always check your answer.
You got d=29.4 miles
Distance+=+Rate%2A+Time
Calculate T%5B1%5D and T%5B2%5D
29.4+=+24%2AT%5B1%5D
29.4+=+18%2AT%5B2%5D
T%5B1%5D= 1.225 hrs.
T%5B2%5D= 1.633 hrs.
Total+Time = 2.858 hrs.,does not equal the 4.9 hr total.
Distance = Rate * Time
When traveling to the town
1. D+=+24%2AT%5B1%5D
When traveling back from town
2. D=18%2AT%5B2%5D
You know that
T%5B1%5D%2BT%5B2%5D=4.9
From equation 1, find a value for T[1]
1. D+=+24%2AT%5B1%5D
D%2F24+=+cross%2824%29%2AT%5B1%5D%2Fcross%2824%29 Multiplicative inverse of 24.
T%5B1%5D=D%2F24
From equation 2, find a value for T[2]
1. D+=+18%2AT%5B2%5D
D%2F18+=+cross%2818%29%2AT%5B2%5D%2Fcross%2818%29 Multiplicative inverse of 18.
T%5B1%5D=D%2F24
Plug those values into your total time equation,
T%5B1%5D%2BT%5B2%5D=4.9
D%2F24%2BD%2F18=4.9Substitute
18D%2B24D=4.9%2A18%2A24 Multiply by the product of 18*24 to remove denominators.
42D=4.9%2A18%2A24Simplify.
cross%2842%29D%2Fcross%2842%29=4.9%2A18%2A24%2F42Multiplicative inverse of 42
D=50.4 miles
Check your answer
1. D+=+24%2AT%5B1%5D
50.4=24%2AT%5B1%5D
T%5B1%5D=40.4%2F24
T%5B1%5D=2.1 hrs.
2. D+=+18%2AT%5B2%5D
50.4=18%2AT%5B2%5D
T%5B2%5D=50.4%2F18
T%5B2%5D=2.8 hrs.
T%5B1%5D%2BT%5B2%5D=4.9
Good answer.