Algebra2D

Word Problems - Theory & Concepts

Techniques and strategies for solving common algebraic word problems including age, mixture, work, motion, and clock problems.

Train A Speed

40 mph

Train B Speed

60 mph

A's Head Start

2 hrs

Dist A: 80.0 mi

Dist B: 0.0 mi

Time (t): 0.00 hr

Let $t$ = time since Train B started (hrs).

Train A's time = $t + 2$ hrs.

Train A's rate = $40$ mph.

Train B's rate = $60$ mph.

Distance A:

d_A = 40(t + 2)

Distance B:

d_B = 60t

60t = 40(t + 2)

60t = 40t + 80

20t = 80

t = \frac{80}{20}

Time to catch up: 4.00 hours

Verify distance:

d_B = 60 × 4.00 = 240.00 mi

d_A = 40 × (4.00 + 2) = 240.00 mi

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