Question

Points P, Q, R, and S appear in that order on a line. The ratio

PQ QR is 3: 4, and the ratio QR : RS is 2: 5. The length PQ
is 6 in. Find the length PS.

Answer 1

Step-by-step explanation: The answer is 8/21 if I'm correct.

Answer 2

the length of PS is 34 inches.

Explanation:

Let's start by using the given ratios to find the length of QR and RS.

We know that the ratio PQ : QR is 3 : 4, so we can write:

PQ/QR = 3/4

Cross-multiplying, we get:

4 * PQ = 3 * QR

Dividing both sides by 3, we get:

QR = (4/3) * PQ

QR = (4/3) * 6

QR = 8

So the length of QR is 8 in.

We also know that the ratio QR : RS is 2 : 5, so we can write:

QR/RS = 2/5

Cross-multiplying, we get:

5 * QR = 2 * RS

Substituting the value we found for QR, we get:

5 * 8 = 2 * RS

Dividing both sides by 2, we get:

RS = (5/2) * 8

RS = 20

So the length of RS is 20 in.

Now we can add the lengths of PQ, QR, and RS to find the length of PS:

PS = PQ + QR + RS

PS = 6 + 8 + 20

PS = 34

Therefore, the length of PS is 34 inches.