Mr. and Mrs. Abbott went on a cruise to a tropical island. They spent a total of 27 hours on the cruise ship traveling to and from the island. On Wednesday the cruise ship left its port and traveled at an average speed of 13 mph to the island. On the return trip, the ship traveled by the same route at an average speed of 14 mph. How many miles did the cruise ship travel from its port to the island?
A.378
B.182
C.365
D.196
+118724 I will start you off :)
Let t1 be the time to get to the island and t2 be the time to get back.
Let d be the distance to the island.
t1+t2=27 so t1=27-t2
speed = distanc/time
so
13= d/t1 and 14=d/t2
13t1 = d and 14t2=d
so
13t1 = 14t2
13(27-t2)=14t2
etc
After you get t2 you can sub back into to get d.
+118724 I will start you off :)
Let t1 be the time to get to the island and t2 be the time to get back.
Let d be the distance to the island.
t1+t2=27 so t1=27-t2
speed = distanc/time
so
13= d/t1 and 14=d/t2
13t1 = d and 14t2=d
so
13t1 = 14t2
13(27-t2)=14t2
etc
After you get t2 you can sub back into to get d.
Let the distance from the Port to the Island=d, then we have:
d/13 + d/14=27
Solve for d:
(27 d)/182 = 27
Multiply both sides of (27 d)/182 = 27 by 182/27:
((182×27 d)/(27))/(182) = 182/27×27
182/27×27 = (182×27)/27:
(182×27 d)/(27×182) = (182×27)/27
(182×27 d)/(27×182) = (27×182)/(27×182)×d = d:
d = (182×27)/27
(182×27)/27 = 27/27×182 = 182:
Answer: |
| d = 182, Miles-the distance from the Port to the Island.
