Question

Yobo and Adoki are keen cyclists. Yobo cycles (x - 45) km from Surulereto Sagamu in 3hours. Adoki cycles (x + 15) km from Sagamu to lfe in 7 hours. They both cycles at the same rate. Answer the following questions

Answer 1

To find the speed at which both Yobo and Adoki cycle, we need to establish a relation between their distances and time.

1. **Speed of Yobo:**
- Distance: \( (x - 45) \) km
- Time: 3 hours
- Speed \( V_Y \) = Distance / Time = \( \frac{x - 45}{3} \) km/h

2. **Speed of Adoki:**
- Distance: \( (x + 15) \) km
- Time: 7 hours
- Speed \( V_A \) = Distance / Time = \( \frac{x + 15}{7} \) km/h

Since they are both cycling at the same rate, we can set their speeds equal to each other:

\[
\frac{x - 45}{3} = \frac{x + 15}{7}
\]

Now, let's solve this equation for \( x \).

### Cross Multiplying:
\[
7(x - 45) = 3(x + 15)
\]

### Expanding Both Sides:
\[
7x - 315 = 3x + 45
\]

### Rearranging the Equation:
\[
7x - 3x = 315 + 45
\]
\[
4x = 360
\]
\[
x = 90
\]

### Finding the Speeds:
Now that we have \( x \), we can find the distances and their corresponding speeds.

1. **Distance for Yobo:**
- \( x - 45 = 90 - 45 = 45 \) km
- Speed of Yobo: \( \frac{45}{3} = 15 \) km/h

2. **Distance for Adoki:**
- \( x + 15 = 90 + 15 = 105 \) km
- Speed of Adoki: \( \frac{105}{7} = 15 \) km/h

Thus, both Yobo and Adoki cycle at a speed of 15 km/h.

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