The ratio of Aldo's cycing speed to Jose's cycling speed is 6:5. Jose leaves at 3:00pm and Aldo Leaves at 3:10pm. Aldo is only 2km away from Jose. How fast is each cycling?(make a rate-time-distance chart).
What is the solution
To determine the cycling speeds of Aldo and Jose, we can create a rate-time-distance chart and use algebra.
Let's start by filling in the known information:
- The ratio of Aldo's cycling speed to Jose's cycling speed is 6:5.
- Aldo leaves 10 minutes (or 1/6 hour) after Jose.
- Aldo is only 2 km away from Jose.
Now let's create the rate-time-distance chart:
```
Cyclist Speed Time Distance
------------------------------------------------
Jose 5 t d
Aldo 6 t - 1/6 d - 2
```
In this chart:
- Speed is given in the ratio of Aldo's speed to Jose's speed.
- Time is the duration of cycling.
- Distance is the distance covered by each cyclist.
Since the distance covered by Aldo is 2 km less than Jose, we subtract 2 from Jose's distance, represented as (d - 2) in the chart.
Now we can use the formula: Distance = Speed × Time.
For Jose:
Distance = 5 × t
Note that the time for Jose is simply represented as 't' since he leaves at 3:00 pm.
For Aldo:
Distance = 6 × (t - 1/6)
Here, Aldo's time is represented as '(t - 1/6)' since he leaves 10 minutes (or 1/6 hour) later than Jose.
Since we know that Aldo is only 2 km away from Jose, we can set up an equation:
5t = 6(t - 1/6) - 2
Now we can solve the equation to find the value of t:
5t = 6t - 1 - 2
5t - 6t = -3
-t = -3
t = 3
Once we have the value of t, we can substitute it back into the equations from the rate-time-distance chart to find the distances covered by each cyclist and calculate their respective speeds.
For Jose:
Distance = 5 × 3 = 15 km
For Aldo:
Distance = 6 × (3 - 1/6) = 6 × (17/6) = 17 km
Thus, the cycling speed of Jose is 5 km/h, and the cycling speed of Aldo is 6 km/h.