Understanding Travel Modes and Rainy Day Choices

The question asks us to determine how many people cycled to work specifically on a rainy day based on the provided survey data and notes. To answer this, we need to analyze the total number of people who cycle and consider the special condition mentioned for rainy days.

Analyzing the Survey Data

The table shows the number of people using different modes of travel to work:

From the table, we see that a total of 72 people cycled to work.

Considering the Notes

Two notes are provided, but only one is relevant to calculating the number of cyclists on a rainy day:

• Note (a): 1 in 8 of the people who cycled to work were over 65. (Not relevant to the rainy day question).
• Note (b): 1 in 3 of the Cyclists stated that they travelled to work by bus on rainy days. (This is the key information).

Note (b) tells us that some of the people who normally cycle change their mode of transport on rainy days. Specifically, one-third of the total cyclists switch to travelling by bus.

Calculating Cyclists on a Rainy Day

To find out how many people cycled on a rainy day, we need to:

1. Determine the number of cyclists who switch to the bus on rainy days.
2. Subtract this number from the total number of people who cycle.

Step 1: Calculate the number of cyclists who travel by bus on rainy days

According to Note (b), 1 in 3 of the total cyclists travel by bus on rainy days. The total number of cyclists is 72.

Number who switch to bus = $\frac{1}{3} \times \text{Total Cyclists}$

Number who switch to bus = $\frac{1}{3} \times 72$

Number who switch to bus = $\frac{72}{3}$

Number who switch to bus = $24$

So, 24 people who normally cycle travel by bus on rainy days.

Step 2: Calculate the number of people who cycled on a rainy day

The people who cycled on a rainy day are the ones who did *not* switch to the bus. This is the total number of cyclists minus the number who switch to the bus.

Number who cycled on rainy day = $\text{Total Cyclists} - \text{Number who switch to bus}$

Number who cycled on rainy day = $72 - 24$

Number who cycled on rainy day = $48$

Therefore, 48 people cycled to work on a rainy day.

Conclusion

Based on the survey findings and the specific note about rainy days, the number of people who cycled to work on a rainy day is 48.

Revision Table: Travel Survey Analysis

Additional Information: Survey Data Interpretation

Survey data like this helps understand commuting patterns. Often, surveys include conditional questions, like how travel changes based on weather or other factors. In this case, Note (b) provides a specific condition (rainy days) that affects the travel mode (cycling vs. bus) for a subgroup of the surveyed population (cyclists).

It's important to read all notes carefully to identify which ones are relevant to the specific question being asked. Note (a), regarding age, was extra information not needed for the rainy day calculation. By focusing only on the note about rainy days, we can correctly determine the number of cyclists under that specific condition.