Let's denote:
- bbb = speed of the boat in still water (km/h)
- ccc = speed of the current (km/h)
- ddd = distance covered (km)
Given:
- Time taken upstream = 8 hours 48 minutes = 8+4860=8.88+\frac{48}{60}=8.88+6048=8.8 hours
- Time taken downstream = 4 hours
Step 1: Express speeds upstream and downstream
- Speed upstream = b−cb-cb−c
- Speed downstream = b+cb+cb+c
Step 2: Use the formula
distance=speed×time\text{distance}=\text{speed}\times \text{time}distance=speed×time
Since the distance is the same,
d=(b−c)×8.8=(b+c)×4d=(b-c)\times 8.8=(b+c)\times 4d=(b−c)×8.8=(b+c)×4
Step 3: Set up the equation
8.8(b−c)=4(b+c)8.8(b-c)=4(b+c)8.8(b−c)=4(b+c)
Expanding:
8.8b−8.8c=4b+4c8.8b-8.8c=4b+4c8.8b−8.8c=4b+4c
Bring like terms together:
8.8b−4b=4c+8.8c8.8b-4b=4c+8.8c8.8b−4b=4c+8.8c
4.8b=12.8c4.8b=12.8c4.8b=12.8c
Divide both sides by ccc:
4.8bc=12.84.8\frac{b}{c}=12.84.8cb=12.8
bc=12.84.8=12848=83\frac{b}{c}=\frac{12.8}{4.8}=\frac{128}{48}=\frac{8}{3}cb=4.812.8=48128=38
Final answer:
The ratio between the speed of the boat and the speed of the current is:
8:3\boxed{8:3}8:3
