萨姆（Sam）每天早晨的日常活动是先吃早餐然后去上班。他驾车出行。
在特定的一天，萨姆于早上 8:00 离开家，并于早上 8:15 到达吃早餐的地方。
他于早上 8:30 离开早餐店。他于早上 9:00 到达办公室。萨姆整个行程的平均速度是 42 km/h。
他从家到早餐店的平均速度比从早餐店到办公室的平均速度快 10 km/h。
求早餐店与萨姆办公室之间的距离。 答案 ...km

1. Convert the journey times into hours and find the total distance for the whole journey.

From home to breakfast place: $15$ minutes $=\dfrac{1}{4}$ h.

From breakfast place to office: $30$ minutes $=\dfrac{1}{2}$ h.

From 8:00 am to 9:00 am, total time $=1$ h.

Average speed for the whole journey $=42$ km/h, so
$\text{total distance}=42\times 1=42\text{ km}.$

2. Form an equation using the two parts of the journey.

Let the average speed from the breakfast place to the office be $x$ km/h.

Then the average speed from home to the breakfast place is $(x+10)$ km/h.

Distance from home to breakfast place:
$\dfrac{1}{4}(x+10)$

Distance from breakfast place to office:
$\dfrac{1}{2}x$

Since the total distance is $42$ km,
$\dfrac{1}{4}(x+10)+\dfrac{1}{2}x=42.$

3. Solve the linear equation for the speed from the breakfast place to the office.

$\dfrac{1}{4}(x+10)+\dfrac{1}{2}x=42$

Multiply by $4$:
$x+10+2x=168$

$3x=158$

$x=\dfrac{158}{3}.$

4. Find the required distance from the breakfast place to the office.

Distance from breakfast place to office:
$\dfrac{1}{2}\times \dfrac{158}{3}=\dfrac{79}{3}=26\dfrac{1}{3}.$