Rowing Boat, Current and Speed

Understanding “Rowing Boat, Current, and Speed” problems in GMAT preparation requires familiarity with the relationship between relative speeds. Here’s a detailed explanation with examples:

Key Concepts:

1. Still Water Speed (Rowing Boat Speed):
   The speed of the boat in still water, denoted as B.
2. Current Speed:
   The speed of the current, denoted as C.
3. Downstream Speed:
   When the boat moves with the current:$$\text{Downstream Speed}=B+C$$
4. Upstream Speed:
   When the boat moves against the current:Upstream Speed=B−C $$\text{Upstream Speed}=B-C$$
5. Time and Distance Relationship:
   The formula connecting Distance (D), Speed (S), and Time (T) is:S=D÷T T=D÷S

Example 1: Finding the Speed of the Current

A boat can row 20 miles downstream in 2 hours and the same distance upstream in 4 hours. What are the speeds of the boat in still water and the current?

Solution:

• Downstream Speed:

S_down = 20 ÷ 2 = 10 mph

• Upstream Speed:

S_up = 20 ÷ 4 = 5 mph

From the formulas:

B + C= 10 (Downstream speed)

B−C=5 (Upstream speed)

Adding the equations:

2B=15  ⟹  B=7.5 mph

Subtracting the equations:

2C=5  ⟹  C=2.5 mph

Boat Speed in Still Water: 7.5 mph
Current Speed: 2.5 mph

Example 2: Calculating Time to Travel

A boat rows upstream at 6 mph and downstream at 10 mph. How long will it take to cover 48 miles downstream and 48 miles upstream?

Solution:

• Downstream Time:

T_down=48÷10=4.8 hours

• Upstream Time:

T_up=48÷6=8 hours

• Total Time:

T_total=T_down+T_up=4.8+8=12.8 hours

Example 3: Distance Covered

If a boat travels for 3 hours downstream at an effective speed of 12 mph and for 2 hours upstream at an effective speed of 8 mph, what is the total distance covered?

Solution:

• Downstream Distance:

D_down=12×3=36 miles

• Upstream Distance:

D_up=8×2=16 miles

• Total Distance:

D_total=D_down+D_up=36+16=52 miles

Practice Tips:

• Label variables clearly. For example, assign $B$ for the boat speed, $C$ for the current speed, and write formulas first.
• Use consistent units. Ensure distances, speeds, and times match (e.g., miles per hour and hours).
• Recheck calculations. Simple arithmetic errors can lead to wrong answers.

Would you like me to create more examples or provide a formula summary?