Advanced Word Problems • Topic 3 of 5

Motion Problems

Motion problems rest on one relationship: distance = speed × time. Rearrange it for whatever is missing — time = distance/speed, speed = distance/time. Keep units consistent (miles with mph and hours). When two objects move, combine speeds: travelling toward or away from each other, the gap changes at the sum of their speeds; chasing in the same direction, at the difference. So two cars in opposite directions for t hours are (s₁ + s₂)·t apart. Read which quantity is asked, substitute into the right form of d = st, and watch that the times and units line up.

Distance equals speed times time on a travel linedistance = speed × timeStartEndspeed (mph)over a given time (hours)

✅ Solved examples

1. A car goes 60 mph for 3 hours. Distance?
d = 60 × 3 = 180 miles.
2. A train covers 240 miles at 40 mph. Time?
t = 240/40 = 6 hours.
3. A runner covers 30 miles in 5 hours. Average speed?
s = 30/5 = 6 mph.
4. Two cars leave a point in opposite directions at 50 and 40 mph. Apart after 2 h?
(50 + 40) × 2 = 180 miles.

✏️ Practice — try these, take hints as needed

1. A car travels at 70 mph for 4 hours. Distance?
d = s × t.
70 × 4.
—
280 miles.
2. A bus covers 150 miles at 50 mph. Time?
t = d/s.
150/50.
—
3 hours.
3. A cyclist covers 48 miles in 4 hours. Speed?
s = d/t.
48/4.
—
12 mph.
4. Two trains leave a station in opposite directions at 60 and 45 mph. Apart after 3 h?
Gap grows at 60 + 45.
105 × 3.
—
315 miles.
5. A plane flies 600 miles at 300 mph. Time?
600/300.
—
—
2 hours.

📝 Topic test — 8 questions

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