Question

Tom and Jimmy plan to leave at the same time from home and

Answer 1

To find the distance between the homes of Tom and Jimmy, it is assumed

that the distances from their home to the café are equal.

• The distance between Tom and Jimmy's home is $\underline{1,617.\overline 7 \ meters}$<u />

Reasons:

The direction in which Tom and Jimmy walks = Towards each other

The speed at which Tom walks = 52 meters per minute

The speed with which Jimmy walks = 70 meters per minute

The time at which Tom leaves = 4 minutes earlier than Jimmy

The point at which they meet = The café

The rate of their speed = Constant

Required:

The distance between Tom and Jimmy home.

Solution:

Tom and Jimmy had a plan to walk at the same speed and meet up at the café.

We have;

The café is equal distance from Tom and Jimmy's houses.

Which gives the following simultaneous equation.

52 × (4 + t) = The distance of Tom's house from the café

70 × t = The distance of Jimmy's  house from the café

• 52 × (4 + t) = 70 × t

52 × 4 = 70 × t - 52 × t = 18 × t

$\displaystyle t = \frac{52 \times 4}{18} = \frac{104}{9} = 11.\overline{6}$

The time it take Jimmy to reach the café, t = $\mathbf{11.\overline6}$ minutes

The distance between their homes, d = 52 × (4 + t) + 70 × t

∴ d = 52 × (4 + $11.\overline6$) + 70 × $11.\overline6$ = 1,617.$\mathbf{\overline 7}$

• The distance between Tom and Jimmy's home = 1,617.$\overline 7$ meters

Learn more about simultaneous equations here:

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