Write 868 million in the form $\alpha \times 10^n$, where $n \in \mathbb{Z}$ and $1 \leq \alpha < 10$, $\alpha \in \mathbb{R}$ - Junior Cycle Mathematics - Question 3 - 2017

Given that the radio signal takes approximately 1-3 seconds to travel 380 000 km:

The speed can be calculated using the formula:

[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} ]

Using the maximum time of 3 seconds:

[ \text{Speed} = \frac{380000 \text{ km}}{3 \text{ sec}} = 126666.67 \text{ km/sec} ]

To convert speed into km/min:

[ \text{Speed} = 126666.67 \text{ km/sec} \times 60 \text{ sec/min} = 7600000 \text{ km/min} ]

Expressing it in the form $\alpha \times 10^n$:

$7.6 \times 10^6$ km/min.

Using the speed found in part (b), which is $7.6 \times 10^6$ km/min:

To find the time, we can use the formula:

[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} ]

Thus,

[ \text{Time} = \frac{868 \times 10^6 \text{ km}}{7.6 \times 10^6 \text{ km/min}} = 114.47 \text{ minutes} \approx 49 \text{ minutes} ]