Question

2 rowing teams are having a race. Boat a had a head start crossing the start line first & traveling at a speed of 3 meters per second. Boat b waited and crossed the start line 6 seconds after boat a. The speed of boat b was 4.8 meters per second.

Answer 1

Question:

Two rowing teams are having a race. Boat A had a head start, crossing the start line first and traveling at a speed of 3 meters per second. Boat B waited and then crossed the start line 6 seconds after Boat A. The speed of Boat B was 4.8 meters per second.

Part A- Write two equations, one for Boat A and one for Boat B. In both equations, let t equal the time in seconds since Boat A crossed the start line and d equal the distance traveled in meters.

Part B- Solve the system of equations from part A. show your work

Answer:

A. Equations

`d = 3t`

`d = 4.8t - 28.8`

b.

`t = 16`

`T = 10`

`d = 48km`

Explanation:

For Boat A:

`Speed = 3m/s`

`Time = t`

For Boat B:

`Speed = 4.8m/s`

Boat B waited 6 seconds later. So, the time is:

`T = t - 6`

Solving (a): Equations

Speed is calculated as:

`Speed = (Distance)/(Time)`

For Boat A:

`3 = (d)/(t)`

Make d the subject

`d = 3t`

For Boat B:

`4.8 = (d)/(T)`

Make d the subject

`d = 4.8T`

Substitute t - 6 for T

`d = 4.8(t - 6)`

`d = 4.8t - 28.8`

Hence, the equations are:

`d = 3t`

`d = 4.8t - 28.8`

Solving (b): The value of d

`d = 3t`

`d = 4.8t - 28.8`

Substitute 3t for d in the second equation

`3t = 4.8t - 28.8`

Collect like terms

`3t - 4.8t = - 28.8`

`- 1.8t = - 28.8`

`1.8t = 28.8`

Solve for t

`t = 28.8/1.8`

`t = 16`

Recall that:

`T = t - 6`

`T = 16 - 6 = 10`

Next, calculate the distance:

`d = 3t`

`d = 3 * 16`

`d = 48km`

So:

Boat A travels for 16 seconds

Boat B travels for 10 seconds

The distance is 48km