# Math Help - Algebra - Speed, Distance Word Problem

1. ## Algebra - Speed, Distance Word Problem

Any help with this one? Those are the equations I have below, yet still cannot seem to figure this one out.

Jessica drove her car at a certain speed for the first 4 hours and increased its speed by 10 miles/hr, for the next two hours. If the total distance traveled by her was 500 miles, find the speeds at which Jessica drove her car at different times.

V1 = D1 / T1

V2 = V1 + 10

T1 = 4
T2= 2

Ttot = T1 + T2 = 6

Dtot= D1+D2 = 500

Vavg = Dtot / Ttot = 83 1/3

What I did was..

[(V1+V2) / 2 ] = Vavg

[((D1/4)+((D1/4)+10))) / 2 ] = Vavg

Solved for D1 then solved for V1 and got 78 1/3. Checked my math and is correct.

Is there any other way to solve this or did they just approximate in the answers?

These are possible answers:

80 and 90 miles/hr respectively
60 and 80 miles/hr respectively
50 and 60 miles/hr respectively

2. Originally Posted by guest84
Any help with this one? Those are the equations I have below, yet still cannot seem to figure this one out.

Jessica drove her car at a certain speed for the first 4 hours and increased its speed by 10 miles/hr, for the next two hours. If the total distance traveled by her was 500 miles, find the speeds at which Jessica drove her car at different times.

V1 = D1 / T1

V2 = V1 + 10

T1 = 4
T2= 2

Ttot = T1 + T2 = 6

Dtot= D1+D2 = 500

Vavg = Dtot / Ttot = 83 1/3

What I did was..

[(V1+V2) / 2 ] = Vavg

[((D1/4)+((D1/4)+10))) / 2 ] = Vavg

Solved for D1 then solved for V1 and got 78 1/3. Checked my math and is correct.

Is there any other way to solve this or did they just approximate in the answers?

These are possible answers:

80 and 90 miles/hr respectively
60 and 80 miles/hr respectively
50 and 60 miles/hr respectively
1. J. drove the car at a speed of v for 4 hours, that means she covered a distance of 4 v;
then she drove the car at a speed of (v + 10) for 2 hours, that means she covered a distance of 2v + 20.

2. Both distances must add up to 500:

$4v + 2v +20 = 500$

3. Solve for v.

3. Originally Posted by guest84
Any help with this one? Those are the equations I have below, yet still cannot seem to figure this one out.

Jessica drove her car at a certain speed for the first 4 hours and increased its speed by 10 miles/hr, for the next two hours. If the total distance traveled by her was 500 miles, find the speeds at which Jessica drove her car at different times.

V1 = D1 / T1

V2 = V1 + 10

T1 = 4
T2= 2

Ttot = T1 + T2 = 6

Dtot= D1+D2 = 500

Vavg = Dtot / Ttot = 83 1/3

What I did was..

[(V1+V2) / 2 ] = Vavg

[((D1/4)+((D1/4)+10))) / 2 ] = Vavg

Solved for D1 then solved for V1 and got 78 1/3. Checked my math and is correct.

Is there any other way to solve this or did they just approximate in the answers?

These are possible answers:

80 and 90 miles/hr respectively
60 and 80 miles/hr respectively
50 and 60 miles/hr respectively
$\text{Speed} = \frac{\text{Distance}}{\text{Time}} \implies \text{Distance} = \text{Speed} \times \text{Time}$

For the first four hours, she drives at an unknown speed, lets call it $v_1$. So using the formula:
$\text{Distance}_1 = 4v_1$

For the next 2 hours she drives at an increased speed. Lets call this $v_2$. So using the formula:
$\text{Distance}_2 = 2v_2$

But $v_2$ is 10 more than $v_1$.
$\text{Distance}_2 = 2(v_1+10)$

The total distance travelled is the combination of the distance traveled over the two times segments. We are given the total distance as 500 miles.
$\text{Distance} = \text{Distance}_1 + \text{Distance}_2$
$500 = 4v_1 + 2(v_1+10)$

Solving for $v_1$ will give you the speed for the first four hours. Then using the fact given about how much the speed is increased, work out $v_2$ which is the speed for the next two hours.